9:40 AM PT -- CoCo's in trouble ... 'cause Conor's taken notice, saying he's totally down for a fight ... and even threw Mark Wahlberg into the mix as well!!!

"Challenge accepted Conan!" Conor tweeted. "I'll whoop you and Walhberg (sic) in the same night."

"Double shares for the Double Champ!"

If Conor McGregor REALLY wants a piece of the UFC, he's gonna have to get through Conan O'Brien first!!

CoCo was leaving UCLA on Wednesday after participating in a college signing day event with Michelle Obama when we brought up the fact he happens to be a minority owner of the UFC.

And, with Conor making so much noise about wanting an ownership stake in the company, we asked Conan if he would follow Mark Wahlberg's lead and offer to sell Conor a piece of his share.

"I will fight him for his [share]," Conan joked ... "If he can take me in the Octagon!"

O'Brien continued to tease ... saying he'd have to look at the paperwork before making any serious deal with Conor.

Look, he's obviously joking the whole way through -- but Conor wasn't kidding when he demanded ownership.

In fact, Conor still isn't signed on to take another fight in the Octagon after retiring via social media earlier this year.