Sources close to the situation tell TMZ ... Nicki and hubby Kenneth Petty had barely walked into the high-end clothing store, Maxfield in WeHo, last weekend when Meek immediately gave them a nasty stare-down.

Like anyone running into an ex, Nicki and Kenneth took offense to Meek giving them a dirty look and that's what triggered the shouting match. Our sources say Nicki and Kenneth did NOT approach Meek by any means. The couple just happened to cross Meek's path when they walked into the store.

This, of course, disputes Meek's side of the story. As we first reported ... the "Championships" rapper said Nicki and Kenneth approached him and started getting loud.

As for Meek allegedly requesting the couple for a word in private, our sources call BS on Meek being this cordial ... since he's the one who started the showdown. Our sources are adamant Meek's still obsessed with Nicki ... while Nicki moved on a long, long time ago.

Our sources say Meek's so petty ... he seemingly mocked Kenneth, who back in March was shown at a carnival hitting a boxing machine arcade game. Meek followed suit several months later ... even talking smack to the punching bag.

And, it's Meek who, back in early March, allowed NBA star James Harden to preview one of his new tracks on Instagram. The track included the lyrics "This s**t beyond me, you was supposed to be my Beyoncé, now you this n***a fiance?!"

Fans were quick to say Meek was referring to Nicki. He later denied the line's about Nicki.