Pictures from the event appeared to show Conor and Machine Gun Kelly being kept apart by security.
The former UFC champion attended the ceremony at the Barclays Centre in New York with his partner Dee Devlin, while the US musician arrived with his Hollywood actor girlfriend Megan Fox.
Following the red carpet altercation, the Dublin-born fighter insisted that “nothing” had happened.
“Absolutely nothing. I don’t know. He showed up, and I don’t know. I don’t know the guy,” Conor told Entertainment Tonight,
“Nothing happened with me, I only fight real fighters, people that actually fight, you know what I mean.
“I certainly don’t fight little vanilla boy rappers. I don’t even know the guy. I don’t know anything about him, except that he’s with Megan Fox.”
Machine Gun Kelly, whose real name is Colson Baker, was also asked about the alleged altercation but walked away without answering the question.
Both men later appeared during the VMAs ceremony.
Conor, who is walking with a cane after suffering a serious leg injury in his latest fight in July, was on hand to award Justin Bieber his artist of the year prize.
Machine Gun Kelly was also among the night’s winners, taking home the prize for best alternative in recognition of his song My Ex’s Best Friend.
He and Transformers star Megan have been dating since last year.