Word started spreading over the weekend that JENNIFER LOPEZ and ALEX RODRIGUEZ had broken up, but it’s not true.  Yet.

They DID release a statement saying that they’re, quote, “working through some things” . . . so it might just be a matter of time.

A source says they “hit a rough patch.”  But before you say what’s obviously in your head, it doesn’t sound like there’s a third party involved.

Not even MADISON LECROY from the Bravo reality show “Southern Charm”.  There were rumors last month that A-Rod was hittin’ that, but a source says those rumors had nothing to do with his issues with J-Lo.

Jennifer and Alex have been together for about four years.  They got engaged in the Bahamas in March of 2019.

J-Lo responded to the rumors yesterday with a video montage set to “Pretty [B-word] Freestyle” by Saweetie.

And TMZ caught up with Alex yesterday, and he told them he’s NOT single.