Dodgers slugger Matt Kemp is trying to keep silent about the rumors he's hooking up with Khloe Kardashian -- but TMZ Sports has learned there's definitely something cooking between them.
Our Kardashian sources tell us Khloe and Matt are in the early, early stages of a relationship and they're "taking it really slow." Makes sense -- Khloe just filed to divorce Lamar Odom last week.
Monday in L.A., Matt was asked about his "love life" ... and said he was only focusing on baseball -- and when asked specifically about Khloe he said even less. However, Kemp also pumped up the buzz yesterday by posting what many people believed to be the giant Christmas tree at Kardashian HQ ... aka Kris Jenner's house.
We're told the tree in the Instagram is NOT KJ's ... and it's actually Matt's. He lives in the same 'hood as the Kardashians -- and we're told the foyer at his pad is almost identical to theirs.
One source tells us Matt and Khloe have a ton in common -- "same neighborhood, same friends, and same love of family."
Could be a very interesting guest list at the Kardashian Christmas dinner.