Sharon Osbourne Totally Cool With Kelly Being Pals With Simon Cowell

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.