The San Diego Padres "have real interest” in former Cincinnati Reds shortstop Zack Cozart, according to a source. Nick Cafardo of the Boston Globe first connected the Padres to Cozart.

Nothing is imminent, the source said, but the Padres have kept in regular contact with Cozart’s agent.

The Padres are one of the few teams with an obvious hole at shortstop, so their interest in the 33-year-old free agent makes some sense. On the other hand, the Padres clearly are not out of their rebuilding phase yet, and adding the top available shortstop to a deal that is unlikely to cover many truly competitive seasons would seem like an odd fit.

The Padres also have reported interest in the premier first baseman on the market, Eric Hosmer, suggesting that they may be willing to add to the major-league team earlier than many would have expected.