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.