Fitzpatrick feels the Jets are offering him the equivalent of a low-end starter or high-end backup salary, ESPN reported on Monday, saying the sides remained "far apart."
Robert Griffin III met with the Jets last week, but the team termed it "due diligence" and said no contract paramters were discussed.
New running back Matt Forte said he knows Fitzpatrick will be "a big part of" who the Jets are in 2016.
"Based off last year's production, and the way Brandon (Marshall) has talked about the chemistry he's built with Ryan, I would expect and hope it would be him, just based off what they had last year," Forte said on a conference call.
Fitzpatrick had a career year with the Jets under the tutelage of offensive coordinator Chan Gailey last season but, according to 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.
The Jets are not expected to budge from the offer to the 33-year-old journeyman and might turn their attention elsewhere immediately. One option for general manager Mike Maccagnan is a deal with his former boss, Houston Texans general manager Rick Smith, to bring in Brian Hoyer.
Hoyer has one year left on his contract with the Texans at $4 million. He signed a $10.5 million, two-year deal with Houston last spring.
Former second-round pick Geno Smith is under contract for 2016 and his cap number is just over $1.56 million, the final season of his rookie contract. He also failed to wrap up the starting job with Fitzpatrick idle because of a leg injury in the 2015 offseason and preseason.
From Fitzpatrick's perspective, the Jets are lowballing him based on the average salary of starting quarterbacks in the NFL.
Brock Osweiler, he of seven career starts, signed with the Texans for $72 million over four years and $37 million guaranteed in the first two years of the deal.
Kirk Cousins, in his first season as Redskins' starter, signed a franchise tender for $19.6 million in 2016.
Options beyond the Jets might be limited for Fitzpatrick, especially if he would like to start. The Dallas Cowboys, Oakland Raiders, Cleveland Browns, Miami Dolphins and others are considering upgrades of their quarterback depth chart, but none are likely to give Fitzgerald more than a clipboard on game day.