LAKE BUENA VISTA, Fla. — Yu Darvish, the Japanese star right-hander considered the best available starting pitcher on a slow-moving free-agent market, has been doing his homework on potential employers.

That includes the Twins, whose general manager, Thad Levine, has publicly called signing Darvish a “priority.” Levine was assistant GM with the Texas Rangers during Darvish’s first five seasons in North America and has spoken with him multiple times this offseason.

Chris Gimenez, who grew close with Darvish as his personal catcher with the Rangers for parts of two seasons (3.29 earned-run average in 12 starts), has recently spent two separate phone conversations sating Darvish’s curiosity “about everything Minnesota has to offer.”

“I know he was very interested in the vision (the front office) had,” said Gimenez, who still hopes to re-sign with the Twins after taking his free agency last month. “He actually called me right over Thanksgiving break and asked me about the organization. Obviously, he has a very good familiarity with Thad, but he was asking about the coaching staff, the players, the types of rules.”

Rules?

“In Texas we had a ton of rules, (and) he was not necessarily a fan of some of them,” Gimenez said Tuesday by phone from his home in Nevada.

Those included Kangaroo Court clubhouse fines for not being early enough for daily team stretch on the field, wearing footwear with shoelaces on road trips or wearing anything on the road that failed to meet third baseman Adrian Beltre’s exacting standards.

“I told (Darvish) pretty much the only rule we have (with the Twins) is no dress shoes on the road,” Gimenez said. “He said, ‘What if I want to wear dress shoes on the road?’ I said, ‘You’re Yu Darvish. You can do whatever the hell you want.’ ” Related Articles Twins’ playoff rotation set, pretty much

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Darvish, 31, is coming off an embarrassing showing for the Los Angeles Dodgers in his first World Series appearance. He made two starts, including a disastrous Game 7 outing, and recorded a total of 10 outs while posting a 21.60 ERA.

That could drive down his value somewhat — even in light of an SI.com report that Darvish was tipping his slider/cutter against the Houston Astros — but he still compares favorably with fellow free agents Alex Cobb, Jake Arrieta and Lance Lynn in a starting pitching market that appears thin at the top. The Twins, who have never given out a pitching contract averaging more than $14 million a season — Phil Hughes’ three-year, $42 million extension in December 2014 — remain interested.

No offer had been extended as of Tuesday evening, but a person with direct knowledge said talks were ongoing.

“He did ask about the city,” Gimenez said. “I know he’s been there multiple times. I told him the community, the support is just like it is in Texas except I feel like we’re on the cusp of something there. I think that’s something he wants to be a part of, especially now, after he went to the World Series. He really wants another opportunity to maybe redeem himself for that.”

MLB Trade Rumors estimated Darvish would sign a six-year, $160 million deal heading into the offseason, but more recently there has been media speculation out of Texas that perhaps he could be lured back to the Rangers with four years plus an option at roughly $20 million annually.

Darvish’s wife and young family still make their year-round home in the Dallas area.

Levine earned Darvish’s trust during and after the recruiting process, when the Rangers committed $111 million to signing him at age 25. That included a $51.7 million posting fee to the Hokkaido Nippon-Ham Fighters, a step that won’t be necessary this time.

That bond between executive and player, Gimenez said, only grew stronger as Darvish made a “very seamless transition” to the majors, underwent Tommy John surgery and embarked on a lengthy rehabilitation process that saw him return to the mound in 2016. Levine was among Rangers’ front-office employees who took Japanese lessons and in general “offered a lot of different avenues for him to assimilate into our culture,” Gimenez said.

So the catcher wasn’t the least bit surprised when the Twins recently hired Japan-native Masa Abe out of the Diamondbacks’ farm system to be their assistant athletic trainer in the majors.

“Thad has a way with people,” Gimenez said. “He’s got that personality. He’s just got a way of really easing people’s nerves and mind and reaffirming that Darvish is the man there. I think that was a big part of it (in Texas), just that relationship that they have. There’s a lot of trust.”

As Darvish’s now-excellent English improved, he even grew to enjoy Levine’s frequent wisecracks.

“Thad has an ability to lighten the mood, lighten the situation and make something that could potentially be a difficult conversation not as difficult,” Gimenez said. “I think Darvish really appreciates that. Thad had his back from day one. That could be a potential game-changer, a humongous get for the Minnesota Twins.”