He previously visited the Cincinnati Bengals before meeting with the Giants on Tuesday.
Ayers, 28, had 29 tackles, 5.5 sacks and one forced fumble last season in 15 games with three starts.
A former first-round draft pick from Tennessee, Ayers has 142 career tackles, 12 sacks and three forced fumbles.
The 6-foot-3, 274-pounder has 27 career starts in five NFL seasons.
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Aaron Wilson covers the Ravens for The Baltimore Sun