Sharon Osbourne is not a big fan of Simon Cowell after their publicized falling out … but she doesn’t care if her daughter Kelly is chummy with the guy, she tells TMZ.

We ran into SO while she was leaving Kelly’s 40th birthday party in Hollywood … and we just had to know what she thought about Kelly and Simon being buddies after KO talked about it in a recent interview.

When asked her 2 cents on the friendship with Simon — who, again, SO feuded with and had a falling out from their ‘X Factor UK’ and “America’s Got Talent” days … Sharon told us it’s “great” … adding, “I’m happy that she does.”

And no, she didn’t think Kelly should ditch her pal just ’cause mom is not a fan … telling TMZ, “Simon’s fine! Simon’s great!”

Of course … this all came about after Kelly told Us Weekly … “I’d never want to disrespect Simon … he’s set in his ways. Who am I to ever get in the middle of that? And, you know, he had a working relationship with my mom.”

Basically … Kelly said the bad blood is between her mom and Simon, and she doesn’t have any interest in getting in the middle — and they don’t seem to want that either.

The breaking point between SO and SC seemed to be in 2019 … when Sharon claimed Simon canned her from the UK singing competition ’cause she was “too old” … again, she claims.