NEW YORK -- Once the offseason dawned and Trevor May became a free agent for the first time in his career, he rekindled a conversation with one of his most influential pitching coaches from Minnesota, Jeremy Hefner. May peppered his old friend with questions about New York City, knowing Hefner had spent years there as a player and now coach. The two chatted about places to live. They talked about where May might fit into the Mets’ bullpen.

Hefner’s presence, May acknowledged Thursday during an introductory Zoom conference, was one of the most significant reasons why he signed a two-year, $15.5 million deal to come to the Mets. The other?

“To be honest, one of the biggest things was just kind of the buzz around Steve [Cohen] and the purchase of the team and the excitement of all the changes that are happening,” May said. “My immediate reaction was wanting to be a part of something like that.”

In the larger picture, the Mets are hopeful Cohen’s purchase of the team will help them continue to lure free agents to Queens this winter. On a more granular level, May’s day-to-day orbit will revolve closer to Hefner, whose 2021 status is not official, but who is widely expected to return as pitching coach.

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The two met in Spring Training after the Twins hired Hefner as an advance scout in 2017. When May tore his ulnar collateral ligament, he bonded with Hefner, who twice underwent Tommy John surgery himself and who prepped his new pupil on what to expect. That was largely the extent of their interactions until two years later, when Hefner became the Twins’ assistant pitching coach and May returned to full health.

During long hours in the Twins’ bullpen, May and Hefner spoke about how best to improve. May leaned on Hefner’s experience rehabbing from Tommy John surgery, listening as his coach discussed flexibility and pliability as ways to increase his fastball velocity. The two talked about using May's improving heater higher in the strike zone. They dug into his pitch mix, which he established years prior as a starter, talking about what was successful and what wasn’t.

“It was a lot of like, ‘Hey, this isn’t working. Why do you think that is?’” May recalled.

One of the most significant breakthroughs came during a July 17, 2019, game against the Mets, when May allowed a late home run to Dominic Smith on a curveball. For some time, May’s curve had frustrated him as he struggled to differentiate it from his slider.

Smith’s homer finally convinced May to scrap the pitch completely, which he did the following week. From that point forward, May focused on his other three offerings, which improved as he posted a 1.33 ERA the rest of that season.

“He wasn’t living up to the expectation that he had for himself,” Hefner said Thursday morning in a telephone interview. “So taking the curveball away I think narrowed his focus, and he was able to go out with confidence with his three pitches and dominate.”

Over time, those experiences developed into what May defined as a friendship between himself and Hefner. So when May reached free agency for the first time last month, fresh off a year in which he set career highs in average fastball velocity and strikeout rate, he knew whom to call.

“I don’t think of myself as a marketer, but I think that’s a part of the job now,” Hefner said.

In truth, May was already mostly sold on the Mets. An outgoing social media personality, May paid close attention to the buzz Cohen was creating on Twitter by interacting with fans and generating excitement about the team. May’s agents spoke to about “half the league” in free agency, but “there were a lot of teams not ready to move.”

“In terms of [seriousness], I think the Mets were the most serious really quickly,” May said. “And then it was just kind of done.”

Now that it is, May plans to dig in deeper with Hefner in the coming weeks, reconnecting about his throwing program and everything else as he prepares for a high-leverage role alongside Edwin Díaz, Jeurys Familia, Dellin Betances and others in the Mets’ bullpen.

It’s a place he feels comfortable being. When May was in New York earlier this week for his physical, his driver recommended an Italian deli, Benateri’s, in nearby College Point, so May instructed the driver to detour there. He bought a sandwich and posed for photos with the staff, who welcomed him to New York.

“I just had a huge smile on my face for hours,” May said. “I was just like, ‘This is where I’m meant to be.’ I was super excited about it. Just the feel and the atmosphere, it’s something that I’ve been developing myself, and I think this fits right into it.”