The Jets are locked in a testy contract stalemate with incumbent starter Ryan Fitzpatrick and are looking at other quarterbacks in case they part ways with the 33-year-old Fitzpatrick.
Griffin, 26, was the No. 2 overall pick in the 2012 NFL draft and was an immediate hit with the Redskins. But injuries and a large drop in productivity caused him to eventually lose his job to Kirk Cousins and he was the Redskins' No. 3 quarterback all last season.
Washington released Griffin on Monday after being unable to trade him.
Fitzpatrick, who set a franchise record with 31 touchdown passes last season, has stated that he wants to remain with the Jets. But the two sides are believed to be far off on what his worth is per a new deal.
According to the NFL Network, Fitzpatrick was offered a contract only slightly better than the three-year, $21 million deal the Philadelphia Eagles gave presumed backup Chase Daniel.
From Fitzpatrick's perspective, the Jets are lowballing him based on the average salary of starting quarterbacks in the NFL.
Cousins signed a franchise tender with the Redskins for $19.6 million in 2016.
The Jets have two quarterbacks on the roster in former starter Geno Smith and inexperienced Bryce Petty.