There is NO reality romance for Tim Tebow -- but he does have a very attractive new female friend. 

Ever since "Chrisley Knows Best" star Savannah Chrisley posted a photo with Tebow at a Sam Hunt concert earlier this week, the Internet went crazy with dating rumors ... especially with Savannah's penchant for dating pro athletes

We happened to see Tim and Savannah at LAX (different flights) -- and both of 'em shut down the dating talk pretty quickly. 

Savannah says Tebow's a great guy, a nice guy ... and her mom already gave him the stamp of dating approval. 

So, maybe something in the future? 

Show Full Image