Free agent cornerback Leon Hall was in New Jersey meeting with the New York Giants on Tuesday, but he left the facility without a deal. Now, the team will have some stiff competition for Hall's services.

Hall, 31, left the Giants and immediately hopped a plane to Atlanta to meet with the Falcons. There are also offers from other team on the table for the former first-round pick.

Hall appeared in 14 games last season for the Cincinnati Bengals. Now that the NFL Draft is over, the market for veteran cornerbacks is expected to pick up. Hall is expected to make real progress on finding a new home this week.

Cornerback Jerraud Powers also met with the Giants last month. He remains a free agent and a viable option, as does Hall.

Pro Football Focus awarded Hall a solid 78.4 grade for his 2015 season, where he played mostly in the slot. New York is currently trying to address that issue on their roster. Free agent addition Janoris Jenkins is more of a ball hawk on the outside, and first-round pick Eli Apple never played as a nickel cornerback at Ohio State.

The Giants want to build up solid depth at the cornerback position.

"The one position that makes me more nervous than anything else is when we don't have enough corners," general manager Jerry Reese said Monday. "Going into this draft it didn't look like we had enough corners back there that had enough experience...We didn't have a lot of proven guys back there. That always makes you nervous because in this league you throw the ball a lot."

New York had major issues in coverage last year, finishing the season as the league's worst-ranked pass defense. The team allowed a whopping 299 passing yards per game tied for 25th in the NFL with 31 touchdown passes allowed. Hall would add another proven body to the mix at CB, though he is not without his question marks.

The veteran underwent back surgery after the season to repair a dis injury. He's also torn his Achilles twice since entering the NFL in 2007. Still, as Reese said, in today's NFL, you can never have enough cornerbacks.

Follow Brandon Katz at @Great_Katzby