More than 1,100 players were released, cut, or waived on Tuesday as teams trimmed their roster to the required 53 men. Now the race is on to claim or sign those who are available, effectively rounding out rosters ahead of the regular season.

The New York Giants put in several waiver claims a year ago but weren't awarded a single player. General manager Joe Schoen certainly isn't going to sit on his hands this time around, so expect Big Blue to be active.

Schoen and head coach Brian Daboll will be on the hunt for anyone they believe will help improve their roster.

With that in mind, here's a look at nine players the Giants should consider claiming or signing through Wednesday's waiver deadline.

CB Caleb Farely

Caleb Farely has some major injury concerns but recently made his way back onto the field. Although still not fully recovered (and carrying a $2.5 million salary if claimed on waivers), he is very familiar to defensive coordinator Shane Bowen. Should Farely go unclaimed, the Giants might be able to sign him for cheap if he's looking for a reunion with Bowen.

CB Desmond King

The 29-year-old Desmond King has a wealth of NFL experience having appeared in more than 100 career games. He would provide a solid, veteran leadership to a very young group. Not only would the former First-Team All-Pro be able to play cornerback, but he is also an accomplished return man -- something the Giants desperately need.

LB KJ Henry

KJ Henry, a fifth-round pick in 2023, doesn't have a boatload of NFL experience but if the Giants wanted to add some youth to their edge rusher pool, he would fit. That would be especially true if they end up trading Azeez Ojulari in the coming days.

Henry is expected to have multiple potential suitors.

S Adrian Amos

Adrian Amos is no spring chicken at this point in his career and 2023 is a season he'd like to forget. Still, the veteran safety would add some stability to a young group and provide leadership that is currently lacking in the secondary. Perhaps a Shane Bowen defense could rekindle what's left of his career.

RB Gary Brightwell

The Giants already walked away from Gary Brightwell, so why would they want him back? Well, they are in need of return men and Brightwell has that experience. He's also familiar with head coach Brian Daboll's offense and would be quick to re-adjust, providing a little extra meat on the bone outside of special teams.

CB Steven Gilmore

When the Giants held joint practices with the Detroit Lions in 2023, cornerback Steven Gilmore, the younger brother of Stephon Gilmore, caught their eye. He not only has the pedigree but has shown flashes of being a quality NFL cornerback. If Big Blue is interested, they most certainly won't be alone.

WR Samori Toure

Wide receiver Samori Toure has already been loosely connected to the Giants with Pat Leonard of the New York Daily News naming him a player to watch. The 26-year-old has limited NFL experience but has flashed a time or two. Leonard also suggests Toure could help the Giants in the return game despite very little history as a return man.

CB Rock Ya-Sin

Rock Ya-Sin has spent the vast majority of his career battling through injuries but has experience in multiple schemes and his veteran leadership could help the Giants' young group. Despite his injury history, Ya-Sin has recorded above-average PFF grades in all but one season and has been a solid tackler at times throughout his career, which is a defensive weakness in East Rutherford.

WR Samson Nacua

Samson Nacua, the younger brother of Puka Nacua, has bounced around from the NFL to USFL to UFL back to the NFL since going undrafted out of BYU in 2022 but he impressed this preseason. Although it wasn't enough to stick with the New Orleans Saints, perhaps his explosive return traits would interest the Giants.

WR Kadarius Toney

Just kidding.

This article originally appeared on Giants Wire: 9 players Giants should consider adding following cutdown day