Fitzpatrick feels the Jets are offering him the equivalent of a low-end starter or high-end backup salary.
Maccagnan said he is willing to improve the team's current offer to the journeyman quarterback.
"We like Ryan -- we'd like to have Ryan back -- but at the end of the day, it's free agency," Maccagnan told reporters Friday on a conference call. "You go through it. At some point in time, hopefully, we can find a middle ground we're both happy with.
"We feel we have a very good situation for Ryan here. He's a very good fit for us. Our goal eventually is to get Ryan under contract and go forward with that."
The Jets have offered Fitzpatrick between $7 million and $8 million per year, according to ESPN sources. Fitzpatrick is thought to be seeking twice that amount.
Fitzpatrick, 33, had a career year with the Jets under the tutelage of offensive coordinator Chan Gailey, throwing for 3,905 yards with 31 touchdowns and 15 interceptions in his first season with the Jets. Fitzpatrick led the Jets to a 10-6 record and set the franchise mark for touchdown passes.
Meanwhile, free agent quarterback Robert Griffin III met with the Jets last week.
"It was more of a meet-and-greet type situation with him," Maccagnan said of Griffin's visit.
Maccagnan mentioned former starter Geno Smith as a fallback option.
"With Geno, we haven't really had him as a starter for us, but he would definitely be a possibility to step in to that role," Maccagnan said.