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Heyman noted Opening Day on April 1 is a “soft deadline” for the two sides.
The Mets acquired the shortstop in a six-player trade from Cleveland in January, but he is eligible to become a free agent next offseason.
Lindor has been open to an extension but has said he didn’t want talks to extend into the season.
“It gets to a point in spring training, and it is time to enjoy the ride and focus on winning,” he told reporters in January.
Mets president Sandy Alderson has also discussed his willingness to sign Lindor to a long-term deal but noted it’s not a sure thing.
“With respect to Lindor, we made the trade. It doesn’t mean necessarily that we are guaranteed to have him long term,” Alderson said last week. “But I think we’re committed to talking about it.”
There could be some caution from both sides considering the 27-year-old has played zero games with his new team. Lindor is also coming off a relatively disappointing 2020 where he had a career-low .258 average with eight home runs in 60 games.
Despite his recent struggles, the four-time All-Star has proved himself as an elite two-way player with two Gold Glove awards and two Silver Sluggers in his first six seasons.
If the Mets don’t sign him this offseason, there will likely be plenty of suitors a year from now.