Mike Gesicki
Gregory Fisher-USA TODAY Sports

The Giants’ rebuild hits its next stage Monday when the NFL’s legal free agency tampering period begins at noon.

After extending quarterback Daniel Jones, franchise tagging running back Saquon Barkley, and amid contract negotiations with both Barkley and defensive lineman Dexter Lawrence, general manager Joe Schoen doesn’t exactly have a gold mine to work with. But it’s not an awful financial situation: the Giants have $16.23 million in space (per Over the Cap) with the anticipated Kenny Golladay release set to clear $6.7 million, plus other cost-cutting moves likely still to come.

So Schoen will definitely be able to operate once the market opens — which free agents could he target with the available cap space?

TE Mike Gesicki. New York committed to Jones by signing him to a new four-year, $160 million contract. Now the front office needs to improve his supporting cast, and one of the main spots to target will be the tight end position.

Daniel Bellinger had a promising start to his rookie year but the Giants need another weapon at that spot, so why not sign a proven veteran like Mike Gesicki?

With the Dolphins last season, Gesicki caught 32 balls for 362 yards and five touchdowns despite his role decreasing. He was on the field for 72% of Miami’s offensive snaps in 2021 before that mark dipped to 45% for the 2022 campaign.

The point is: Gesicki can produce. And the Giants did not have consistent production at the tight end position last season.

Schoen swinging a deal for around $7-8 million per year would make this a great value signing.

LB T.J. Edwards. The Bills’ Tremaine Edmunds is the top inside linebacker in free agency and has the Buffalo connection with Schoen and head coach Brian Daboll, who need major help in the middle of the defense. But he may be too expensive.

One of the next guys on the list is T.J. Edwards, who recorded a whopping 159 combined tackles with the Eagles last season. This tied him for seventh in the NFL in that statistic. Edwards also fares well in pass coverage, having only allowed a combined 82.1 passer rating when targeted last season.

If Schoen could swing a deal that sits right around (or possibly under) a $10 million average value, this could be an enormous acquisition for the Giants. Last season, Big Blue let up 144.2 rushing yards per game, the sixth-worst mark in the league.

OL Ben Powers. The Giants have their franchise left tackle in Andrew Thomas and a hopeful franchise right tackle in Evan Neal, who must improve after an up-and-down rookie season. Right guard Mark Glowinski is also under contract for two more years.

But the left guard and center spots are uncertain, with question marks surrounding the futures of both Nick Gates and Jon Feliciano. The Giants need help on the interior, so that’s where Powers comes in.

Powers started all 17 games and played every single offensive snap for the Ravens last season, and didn’t allow a single sack.

If the Giants want a rock-solid guard they could rely on for the next 2-3 years, Powers might be their guy.

OL Nate Davis. But if Powers doesn’t work out, the Giants could also take a look at Nate Davis, who was a starter for 12 games with the Titans this past season and allowed only three sacks.

There’s a reason he’s the second interior offensive lineman on this list though — his durability issues. Davis hasn’t played a full season since 2020, when he started all 16 games for Tennessee.

That may lower his price on the open market, however. So this could end up being a good value signing for the Giants, who would be acquiring a highly capable starting guard.

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Ryan Honey is a staff writer and host of the Wide Right Podcast.