Looks like the Met Gala tension between Rihanna and A$AP Rocky might've been overblown ... or at least misplaced.

Sources familiar with the situation tell TMZ the woman seen chatting with Rocky on the carpet Monday night in now-viral video is Giovanna Battaglia Engelbert ... the Italian fashion editor and stylist who's known Rihanna for years and who has "a lot of respect" for her.

We’re told the clip making the rounds online doesn’t show the full interaction ... because Giovanna was actually talking with Rihanna first -- and the two were laughing together before she continued the conversation with Rocky nearby.

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According to sources ... Giovanna -- who attended the Met Gala with singer EJAE -- was joking around with Rocky about his necklace while Rihanna handled an interview a few feet away. The video sparked speculation online after Rihanna appeared serious while turning toward Rocky mid-convo ... but insiders insist there was zero romantic energy between Rocky and Giovanna.

But that wasn't the only evidence of a tiff that night. TMZ broke the story Tuesday ... RiRi and Rocky were filmed by a photog having an emotional discussion inside their Sprinter bus after the event and, at times, they seemed a bit annoyed with each other.

So, despite social media trying to turn a fashion-world convo into relationship drama, we're told there was nothing going on here besides Met Gala small talk.