The 35-year-old infielder is one of several players general manager Al Avila has discussed with rival teams.
"I've already exchanged several phone calls before coming here on several guys, Kinsler being one of them," the executive told Evan Woodbery of MLive.com.
Kinsler is one of the few veterans remaining on a team looking to rebuild, and predicted trade talks would be a big part of his offseason.
"There were a lot of rumors last winter. There were a lot of rumors during the season. There's going to be a lot of rumors again," Kinsler told Jason Beck of MLB.com.
Kinsler, a four-time All-Star and 2016 Gold Glove winner, posted the lowest OPS (.725) of his 12-year career last season, hitting 22 home runs and driving in 52 across 139 games.
The veteran is under contract for one more season and is set to earn $11 million.
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