FRISCO, Texas — If Alabama and Auburn will play an Iron Bowl this weekend, and Ole Miss and Mississippi State’s football teams will square off in the Egg Bowl, then perhaps the New York Giants’ Thanksgiving visit to the Dallas Cowboys is ripe for naming as well.

Might we suggest: The Odell Beckham Jr. Bowl?

The framework isn’t as simple as, well, winner gets the three-time Pro Bowl receiver who’s returning from a February ACL injury and expected to sign with a team soon. But the pair of 7-3 NFC East teams facing off on Thursday appear to be the leading contenders for his services.

NFL Network’s Ian Rapoport reported Monday that Beckham has plans to visit each club after Thanksgiving, the Giants offering an opportunity to return to his five-year home while Dallas and Beckham, Rapoport characterized, have “so, so, so much mutual interest.”

And we need not rely on reports for this hunch. Because the Cowboys — from team owner Jerry Jones to head coach Mike McCarthy to quarterback Dak Prescott to Defensive Player of the Year favorite Micah Parsons — have told us themselves.

The Cowboys aren’t subtle

Prescott, until Tuesday, had been the most subtle. He’d let his teammates and Jones publicly vie for the receiver who’s back on the market after a three-month stint with the Los Angeles Rams that included five touchdowns in eight regular-season games, two more in the postseason and a Lombardi Trophy.

Prescott hadn't tweeted at Beckham like Parsons had, nor waxed poetic in interviews like receiver CeeDee Lamb or team brass. The quarterback had acknowledged interest firmly but concisely. Until Tuesday. It was then, standing at his locker after walkthrough practice, that Prescott confirmed he has exchanged messages with his fellow Louisiana native.

“Definitely I've sent some messages,” Prescott said, when pressed. “It's been a little back and forth. Just making sure he understands that we want him here. As I said before, it's a business. But right now, I guess it's who can recruit better. Yeah, I don't know necessarily about what he's looking for when it comes to the numbers and long term and all that, but I know that we want him here and hoping it all works out.”

Prescott characterized the interest as, “mutual, honestly. Mutual.” Business and contract figures will come into play, he agreed, “but I'm feeling like it’s mutual.”

Jones, speaking Tuesday during his regular radio show, mentioned Beckham for what must be at least the dozenth time. He declined to get into negotiation points, beyond saying that if Beckham’s health and financial goals weren’t at least plausible, Dallas wouldn’t be preparing to bring Beckham to the facility for a visit. Jones had said Sunday that he believed the Cowboys looked like a Super Bowl-caliber squad in a 40-3 blowout of the Minnesota Vikings. Tuesday, he indicated that comment was connected to his pursuit of Beckham.

Sure, the Cowboys’ 7-3 record equals that of the Giants, the Cowboys’ head-to-head victory giving them the playoff edge entering Thursday. But Vegas also far favors the Cowboys’ Super Bowl chances over the Giants due to game trends and health. The Cowboys won seven games despite missing Prescott for five with a thumb fracture. Receiver Michael Gallup and running back Ezekiel Elliott have returned from knee injuries, and All-Pro left tackle Tyron Smith could return as soon as December. The Giants, on the other hand, are currently without two starting receivers, two starting offensive linemen, their starting tight end, a starting edge rusher and three starting defensive backs. More are questionable; and yet some, including receivers Sterling Shepard and Wan’Dale Robinson, are lost for the season.

It’s not a stretch to say the Cowboys are trending in a far more positive direction. Should Beckham want a team with more favorable postseason odds, the Cowboys hold a 99% chance of making the playoffs and 15% chance of winning the Super Bowl, per FiveThirtyEight’s playoff predictor (only the Chiefs, at 23%, slot better). The Giants carry a 51% chance at a postseason berth — and a 0.4% chance at a championship, per FiveThirtyEight.

Beckham has indicated interest in playing for a contender. And yet: he seems intrigued by the Giants.

A trip back home

There is, of course, as Giants star running back Saquon Barkley put it, romance to Beckham’s possible return to the team that drafted him 12th overall in the 2014 NFL draft.

Beckham’s five seasons in New York include all three of his Pro Bowl years. He averaged 92.8 receiving yards per game across 59 games, reaching the end zone 44 times. Some of his former teammates, including Barkley and Shepard, would be teammates again should he choose New York. The Giants must determine their contractual futures with Barkley and quarterback Daniel Jones this offseason, but head coach Brian Daboll and offensive coordinator Mike Kafka have impressed the league with creative schemes that maximize personnel.

Barkley laughed at the Cowboys’ hyper-public recruitment, quipping “I don’t have to tweet at him” to let Beckham know how he feels. Barkley said he understands why NFL players would want a talent like Beckham, who’s a “heck of a player.” So why go to the injury-riddled, lost-to-the-Lions-last-week Giants?

“There’s not really a sales pitch,” Barkley said Nov. 11, before that loss. “It’s New York. It’s the Giants. Obviously he has familiar faces within this facility, within this locker room and personally.”

Beckham shouldn’t have an issue finding snaps with the Giants, who sorely need depth at receiver.

“I think it would be a great story to come back to a place he was at before and continue to help build success,” Barkley said. “To come here with the right mindset and be a leader and be the type of player that he can be for this team. Like I said, he’s a special player.”

Receiver Darius Slayton told NFL Network this week that Giants who played alongside Beckham “love him.”

“I’m all for anybody that will help our team,” Slayton said. “So if he wants to come here and sign here, I think he knows where home is. And I’ll leave it with that.”

‘We’ve got a chance’

Thursday, the Cowboys’ run-first offense and pass-rush led defense will host a Giants team that has proved far more scrappy, and schematically challenging, than anticipated in this staff’s first year. The Cowboys are favored by 9.5 points, per BetMGM. But they know how emotions run high in divisional games, how they’ve lost their last three Thanksgiving contests, and how the Giants have exceeded expectations at several junctures this year. Dallas insists it’s not settling after the 37-point victory in Minnesota.

“I just really think we don’t have the type of locker room to even get big-headed,” Ezekiel Elliott said. “I think we’ve all got a lot to prove. We’ve all got a lot to play for. I don’t think any of us are satisfied with being 7-3.

“We know what the bigger plan is, the bigger goal, and we’re not even close to it yet.”

The Cowboys do, meanwhile, hope they’re close to playing alongside rather than just talking at Beckham. Could a deal come as soon as next week? The visit will follow Thanksgiving shortly, it appears.

Until then, Jerry Jones plans to continue reminding Beckham and fans across the country that this Cowboys team has the talent and depth to contend for a Super Bowl. His coaches and players may need to focus on the next game. But the team owner, Jones believes, has his eyes elsewhere.

“The same guy that’s talking about going and getting a receiver, and going out here and making a move like that, right now has got to be thinking past Thursday, wouldn’t you think?” Jones said on Dallas radio station 105.3 The Fan. “The main thing everybody would agree with is, if you can improve this team right now and it’s within reason, then you should do it.

“We’ve got a chance.”

Follow Yahoo Sports’ Jori Epstein on Twitter @JoriEpstein