8:38 AM PT -- Sources with direct knowledge tell TMZ ... Ayo Edebiri and Paul Mescal are just friends.

Paul Mescal and Ayo Edebiri took a photo together to celebrate St. Patrick's Day -- and there's two takeaways ... she's committed to her Irish bit, and they may possibly be a thing.

The "Bear" star has her hand on the Irish actor's shoulder in this picture she threw up on IG to celebrate St. Paddy's Sunday -- and he's pretty into it, with his arm casually draped across her lap.

The grin on Ayo's face kinda says it all ... she's more than comfortable in PM's company.

Fans certainly felt the same vibe ... going into overdrive with speculation that they may be dating. Some called them a cute couple, others said they looked good as friends too.

While the rumor mill is in full swing, this could obviously just be pals hanging out -- as there's no explicit signs of PDA to suggest this is anything romantic. If anything, this might just be Ayo continuing to lean into her "Irish" heritage ... a bit she's been into for a year or so now.

Long story short ... Ayo goes around insisting she's Irish and that she was in "The Banshees of Inisherin" -- and because of her love for Ireland, Ireland seems to love her right back.

Paul, of course, is Irish himself ... and he's known to be friends with Ayo -- so in all seriousness, this is probably just him helping his bud keep the gag going.

Originally Published -- 7:32 AM PT