Sources with direct knowledge tell us the Oscar-winning actress and the Irish star are just pals -- and have been for a long time now -- even though they were looking pretty damn friendly this week in North London.

While we're told they're not romantically involved, Natalie and Paul have clearly struck up quite the friendship ... in fact, our sources say they've known each other for a while.

If you didn't see ... the two actors were hanging out during a smoke break outside Bar 69 on Tuesday -- and the pics started the dating hearsay in the first place, even though there wasn't any PDA.

The light-hearted sighting came after Natalie quietly finalized her divorce from Benjamin Millepied in March -- ending their 11-year marriage ... another reason people thought there was something afoot here between her and Paul ... both whom are single right now.

Natalie's divorce unfolded amid allegations of infidelity on her ex-hubby's part for over a year -- a matter that remains unaddressed to this day by either party ... but she's unattached, and like we said, was looking somewhat cozy with Paul here. Granted ... he does this at times.

You'll recall ... he was recently linked to "The Bear" star Ayo Edebiri following their cozy St. Paddy's Day snap. But even those rumors were quickly disputed, with sources telling us they're just good buds ... the same way he apparently is with Natalie too.

FWIW, they haven't starred in any movies together ... and don't have any on the books either. They did do 'Actors on Actors' together last year -- and they certainly seemed cool then.