Kim Kardashian and Odell Beckham Jr. Hug in Vegas During Fanatics Party

Kim Kardashian and Odell Beckham Jr. made contact this weekend in public -- although, it does seem they're still trying to maintain somewhat of a low profile as a new item.

The rumored couple was spotted in the same vicinity Saturday night at the Fanatics Party at the Marquee Dayclub in the Cosmopolitan -- and TMZ obtained new video that shows them briefly going in for a hug ... albeit, one from which Kim seemed to quickly pull away.

Check out the clip ... you see them go in for a quick, friendly hello -- and Kim almost wraps her right arm around Odell's neck, but quickly yanks it down and away before she can fully wrap her arms around him.

What's interesting about that is ... that same evening Khloe was trying to block cameras from recording KK and OBJ as they all boarded an elevator -- as seen in other footage we also got. So, it feels like they're trying to keep things on the DL.

The weird thing about this is ... if they're really trying to hide their relationship, why even show up in Vegas together at all??? Everyone saw them this weekend, and they were kinda trailing each other all over the place Saturday night, very conspicuously.

If Kim and Odell are, in fact, trying to throw people off the scent of them being together, they're not doing a very good job. Rumors of them dating have been swirling for months.