The Giants hosted Stingily for a visit last week along with Ben Ijalana, so he was clearly on their radar.
Stingily, 27, is a former sixth-round pick of the Titans back in 2011. He played out his four-year, $2,150,500 rookie contract with the Titans before signing a two-year deal with the team back in March.
However, Stingily was among their final roster cuts. The Steelers later signed him to a contract in October, but he never appeared in a game during the 2015 season.