Just hours before Kardashian, 29, filed for divorce Friday morning, citing irreconcilable differences and requesting to drop Odom from her name, she was spotted hitting a private gym in Beverly Hills with L.A. Dodgers outfielder Matt Kemp.
"They are just friends and have been for a long time," a source tells PEOPLE of the relationship buzz, spurred by the baseball star's Instagram post of Kris Jenner's Christmas tree on Thursday. "Khloé is absolutely heartbroken right now [over Lamar] and dating someone is the last thing she's thinking about."
Another Kardashian insider adds: "It could be heading [romantic] in the future, but Khloé wasn't spending time with him when she was still with Lamar. She absolutely wasn't. People need to remember that she and Lamar haven't lived together since June."
Kardashian and Kemp, also 29, at least seem to share a love of music. They attended a Drake concert together on Nov. 25, a John Legend concert on Dec. 1 and saw Jay Z perform on Dec. 9.
Besides, Kemp has practice being the rebound guy. He famously dated Rihanna after her initial split from Chris Brown.
A rep for Kardashian had no comment.