The former Washington Redskins starter-turned-backup visited the Jets on Friday, ESPN NFL Insider Adam Schefter reported.
The Jets are applying due diligence and remain focused on re-signing Fitzpatrick, according to a league source.
Fitzpatrick and the Jets are far apart in negotiations. The Jets are believed to be offering between $7 million and $8 million per year, roughly half of what Fitzpatrick is seeking.
The Jets have also expressed interest in trading for San Francisco 49ers quarterback Colin Kaepernick, but that interest never appeared serious.
They have only two quarterbacks under contract: former starter Geno Smith and second-year player Bryce Petty, who has no regular-season experience.
Fitzpatrick, who arrived last year in a trade with the Houston Texans, led the Jets to a 10-6 record and set the franchise record with 31 touchdown passes. But he's 33, and the team doesn't see him as a long-term solution, which explains the hesitance in contract negotiations.
Griffin, once the face of the Washington franchise, was injured and fell out of favor with two separate coaching staffs. He didn't play last season and was released last week because his $16 million became guaranteed for 2016.
Ex-Washington QB Griffin to visit Jets
ESPN Jets reporter Rich Cimini discusses RGIII's visit to the Jets and what might happen with Ryan Fitzpatrick's contract negotiations.