A report on Monday suggested the American-based owners at Fenway Sports Group (FSG) had produced a sales deck and investment banks Goldman Sachs and Morgan Stanley were assisting the evaluation process.
FSG admits it is open to accepting new shareholders but has not gone as far as to say the club as a whole is on the market, although it has not definitively ruled it out.
A figure in excess of €4billion is expected to be demanded by FSG to sell all their shares in Liverpool, with that figure well out of reach for McGregor despite his success in UFC and boxing.
Yet after hinting he would be interested in buying Manchester United and Chelsea in recent months, he has tweeted that he would like to explore the possibility of being part of a consortium buying Liverpool.
This is far from the first time McGregor has used his Twitter platform to spark debate, with his retirement from UFC quickly followed by messages that he would return to the cage.
If McGrgeor is serious about being part of a deal to buy Liverpool from FSG, he would need to get the backing of lavishly wealthly backers, with Reds legend Jamie Carragher suggesting this is the perfect time to sell the club.
"I think FSG have done a great job at the club, and I don't think they've ever proclaimed to have the funds of Manchester United, Chelsea or Manchester City," he told The Overlap.
"They were the owners who brought the title back, the owners who brought Jurgen Klopp, the stadium has been transformed, the training ground has been transformed. They've almost been a model for clubs like Arsenal.
"I am surprised. Will the club ever be valued as highly as it is right now again? With Klopp as the manager and the team having been so successful over the last few years? Maybe there's something in that.
"I just thought that with so many American owners coming into the league, I thought there was a power play in some ways where they could see something in the future given what we've seen in American sports, so I thought the owners would be here for a while.
"Maybe they woke up on Monday morning and read about how much Manchester City have made commercially and thought, 'you can't stop it, can you?"