TMZ Sports has learned the MLB pitcher chatted up Genie Bouchard at a music festival in Miami just weeks after the tennis star broke up with her longtime BF -- and it's got us all wondering, are the two now igniting a new romance?

We obtained a picture and video of Bouchard with the baseball player at Ultra on Saturday night ... and while we're told there was no kissing, touching or feeling going on -- it seems apparent Harvey was interested in getting her ear.

You'll recall, Harvey has been linked to Bouchard in the past -- back in 2014 while Harvey was starring for the Mets, he reportedly tried to grab tickets to one of Bouchard's U.S. Open matches and potentially meet her afterward.

No word on if the two were ever able to connect back in the day ... but the duo certainly seems to have met now.

Of course, 28-year-old Bouchard is just recently single -- she and Rudolph's split is very fresh -- so it's unclear if she's looking to jump back in the dating pool again.

As for 33-year-old Harvey, he's single ... and has been known to date some very pretty people in the past.