One report suggested the assaulted man, who is in his 50s, is Whelan's father.
McGregor was at the Black Forge Inn in Crumlin, the Dublin suburb where he grew up, when he allegedly threw several punches after a dispute with a group of men on Sunday night.
McGregor is alleged to have tried to hit one member of the group before the associate of Whelan's stepped in and was punched twice by the UFC star.
The reports claim McGregor also punched a third man during the incident before he was escorted out of the pub and into a car.
Irish police say they are not investigating the scuffle. "There is no report on this matter and no complaint from any injured parties, patrons of the pub or the pub itself and no statements were taken," an Irish police spokesman told The Irish Independent.
UFC boss White said on Wednesday the organisation has not received any information regarding McGregor's involvement in the alleged brawl.
"I don't think it's true," White said. "Because if it was true, it would be big. Conor can walk down the street and it's big news now. If this were true, I just have to believe it would be off-the-charts crazy.
"If it's true, we'll end up finding out. I can't chase all these things around. If it's true, we'll get it figured out and we'll go from there."
McGregor, however, has posted a message on social media many fight commentators have interpreted to be the UFC star's quirky way of suggesting he was involved in the brawl.
Irish media outlets reported on Tuesday that a "well known Irish celebrity assaulted a close associate of a senior Kinahan cartel henchman" — but did not mention the 29-year-old mixed martial artist.
Unconfirmed reports claim Whelan has demanded McGregor pay restitution of 900,000 euros (NZ$1.55 million) or he will be shot.
The rumours are not supported by any evidence, however, online fight site craziestsportsfights.com claims to have an unverified audio recording from a source with knowledge of the situation.
The source claimed the altercation at the Black Forge stemmed from an earlier incident where a close friend of McGregor's was targeted. The website admits the audio is unsubstantiated.
"The first girl, Meghan Whelan, so her brother is Graham Whelan out of Crumlin. Also known as The Wig," the audio clip claims. "He's major, so that's not going to end well for him [McGregor]. He went into the pub and he was trying to get at Ryan Burne [another Whelan associate]. Ryan Burne is who he gave the digs [punches] at.
"So Meghan Whelan's dad was in the way, and he ended up getting a boxing to the head as well and he [McGregor] was smashing Ryan Burne up."
The MMA Bible has also reported claims from people claiming to have witnessed McGregor involved in the bar fight.
The news heightens concerns McGregor's fight career is going off the rails. White said McGregor — who hasn't fought since he became the first UFC fighter to hold two championship belts across two weight divisions when he stopped Eddie Alvarez at UFC 205 in November, 2016 — may never fight in the UFC again.
White said the two parties were working on a plan for McGregor to headline the year-ending UFC 219 card before they were derailed by the Dubliner's actions at a Bellator event in Dublin where he invaded the cage and abused a referee.
"We were working on a fight for him at the end of the year. And he's just not ready. Listen: Conor might never fight again. The guy's got a f***ing 100 million dollars," White said.
"These guys make money and that's it. Fighting is the worst. Try to get up and get punched in the face every day when you've got $100 million in the bank. Money changes everything for a lot of people. He's a young, rich kid who is a god in Ireland. That's not the healthiest environment either. It's all part of it."
