Jacob Elordi and Olivia Jade have been rumored to be on the outs -- but we know that's simply not the case ... 'cause the couple's hanging out as he gets ready for a big show.

Sources with direct knowledge tell us JE and OJ are most certainly not broken up -- despite a report claiming otherwise -- and more importantly ... we're told they're literally together in NYC right now, this as Jake goes through rehearsals this week ahead of his 'SNL' gig.

Per production sources ... Olivia has been seen this week in and around 30 Rockefeller Plaza, and we're even told Olivia's been spotted near Jacob's dressing room.

We know Jacob and the 'SNL' team are running through what they're going to put on Saturday -- evidenced in photos, videos and behind-the-scenes clips they're posting on social media -- and it sounds like Olivia Jade is in the mix back there as well with her BF.

The reason folks assumed they'd split -- aside from the report claiming they had -- was because Olivia appeared to have unfollowed Jacob on Instagram ... but TBH, it's unclear if they were even following each other, to begin with.

Jacob and Olivia have been dating for at least a few years now -- and while they did reportedly break up once before ... they ended up getting back together, and we're hearing they continue to be an item right now.

Part of the reason, perhaps, that people are speculating about their status might lie in the fact that Jacob has had a huge year in his career -- starring in two critically acclaimed films ... and paving a path for himself as a bona fide A-lister, outside of his "Euphoria" run.

Again, this all started with people seeing an alleged "unfollow" and the rumors kicked into high gear after that. From what our sources are telling us though ... Olivia's right by Jacob's side as we speak, and she'll probably be hanging around through the weekend as well.

Of course, it'd be big news if either she or Elordi were single ... they're both smoking hot and would be one of the bigger eligible bachelors/bachelorettes on the young Hollywood market.

For the time being, though ... people oughta hold their horses, 'cause they're still on.

Sorry to all the thirsty dreamers out there!