Kim Kardashian Shares Traits She Wants In A Man Amid Odell Romance

Kim Kardashian's marriage with ex-husband Kanye West didn't work out -- but she's open to finding love again ... only, now, she's got a super strict list of qualifications for the next one.

The reality star -- who's rumored to be dating Odell Beckham Jr. right now -- shared what she's looking for in her next man on James Corden's podcast Thursday ... and she says there are a few traits she wants in any new guy she starts dating seriously.

Just a taste of what she wants in her next fella ... being accountable for actions, taking accountability, holding her down, not having to babysit him and finally ... good teeth.

Kim tells JC she's not delusional enough to think that someone will check every single box ... but nonetheless, that's a pretty serious list, so it looks like Odell's got his work cut out for him!

As for whether she'll walk down the aisle again, Kim tells James she ain't sure ... and knows it'll take a  very "special, unique person" to deal with her huge, epic life -- 'cause she realizes it's a massive commitment and doesn't take it lightly. But, it goes without saying .. whoever comes along will have whole lotta fun, that's how KK puts it here anyway.

Now, Kim says she's not desperate for love -- noting she isn't lonely with her 4 kids, her work, and family. Of course, she explains it'd be nice to share her life with someone.

Kim adds that while she's the biggest hopeless romantic out there, she knows what a real relationship is, especially since she's done the marriage thing three times now -- so as for the rumors she's dating OBJ, it looks like she's being cautious and taking it slow.

With that said ... they were last seen out together at the Fanatics Party at the Marquee Dayclub in the Cosmopolitan the past weekend. Even though they were tying to stay on the DL, we peeped them at a bash ... where Kim and OBJ went in for a hug, albeit a slight one.