Here's the deal ... romance rumors have been flying for the past few weeks about the golf pro and the CBS Sports reporter -- this after they've been seen seemingly getting cozy on PGA tours of late, not to mention the fact they're both single ... well Rory certainly is anyway.

Amanda is rumored to be on the outs with her hubby -- and of course, Rory is divorcing his wife ... which makes these pics TMZ Sports got of them on Sunday all the more interesting.

Check it out ... these pics were taken at Hamilton Golf & Country Club in Ontario -- where the Open was being played ... and where Rory did an interview with Amanda.

While everyone was checking out their body language during the interview -- chock-full of smiles and giggling as it was -- the photos we got here, which we're told were shot right at the end of their on-camera chat, seem to tell more of a full story about their vibe BTS.

As you can see ... Rory and Amanda were cheesing it up once the cameras stopped rolling ... and the two of them even shared an embrace. No real PDA beyond that, though.

Like we said ... people think these two are an item now, and while neither of them has addressed the speculation head-on ... there have been reports they're just pals/professional.

Hard to say if these pics prove the case either way ... but it raises an eyebrow for sure.

Anyhoo ... we're sure the golf crowd will continue to speculate -- fact is, they're both good-looking (maybe?) singles ... and they're also in the same field ... quite literally, a golf course.

If they are banging, they sure do make a hot-looking couple ... we'll say that at the very least.