Kim Kardashian and Odell Beckham Jr. are looking more like a couple by the day -- and they seemed to soft-launch their relationship this weekend ... that's what this video suggests.

Check out this footage, obtained by TMZ, that shows Kim and OBJ at Jay-Z and Beyonce's Oscars after-party Sunday night at the Chateau Marmot in L.A. -- and you can see them mingling in a lobby-like area of the venue ... getting touchy-feely with each other.

As you can see ... Kim was chit-chatting with Odell in a pretty flirty manner -- going back and forth with him and seemingly comparing their outfits. At one point she actually puts her hands on Odell too ... going up and grabbing his face, almost as if she's going in for a kiss.

You never actually witness them lock lips ... but this is the most we've seen them interact with one another in public since they've been rumored to be dating ... going back months now.

Doesn't look like they knew they were being filmed either -- but at this point ... it's pretty obvious they're together as a couple. They even showed up together for all the post-Oscars shindigs ... first hitting the Vanity Fair after-party, and later swinging by Jay and Bey's thing.

Remember, they were also spotted out together in Vegas last month during the Super Bowl -- and there, too, they seemed to be trying to lay low ... and distance themselves a bit.

Same vibe here when they were outside heading into a party -- namely, trying to stagger a bit -- but they're not doing a very good job at throwing people off the scent anymore. Now with this new video -- it seems cat's outta the bag ... they're straight up dating each other.

Rumors of Kim and Odell being an item have swirled for months -- and all reports thus far have suggested that it's not that serious. However, they seem pretty into each other ... and the fact they continue to hang out all this time later indicates this might be the real deal.

Kim has yet to publicly declare anyone as her official significant since splitting from comedian Pete Davidson in August 2022. Of course, she was previously married to Kanye West, who she shares kids North, Saint, Chicago and Psalm with ... but that's over.

As for Odell ... he split from his longtime girlfriend Lauren Wood earlier in 2023, and has been single since.

While Kim and Odell have yet to confirm the rumored romance on paper (or on IG, more like) ... it's clear they enjoy each other's company. Perhaps a little bit more than that, TBH.