Norris, a leading gay rights activist, made the claim in interviews to promote his new autobiography and repeats it in the book.
But family, friends and historians have cast huge doubt on the Norris allegations.
Collins’s grand niece, Ireland’s former justice Minister Nora Owen, has dismissed the claims out of hand.
Speaking to the Irish Independent, Owen rejected the claims made by Norris on the basis of conversations he had with one of Collins’s grand-nephews and an elderly man who claimed to be one of the rebel’s boyfriends.
Owen questioned whether Norris had checked that his claim was correct.
She said: “I don’t know which grand-nephew provided Mr Norris with his information.
“It doesn’t matter whether Michael Collins was gay or not but that Mr Norris’s claims are hearsay.
“There’s absolutely no gossip, talk, anything in the family that would sustain any such an argument.
“It’s not that I’m against gays or anything, it’s just that we have no evidence at all to say that Michael Collins was a gay man.”
The former Minister added: “It didn’t matter to us but it certainly wasn’t something that anybody, my mother or my aunts - Michael’s nieces - ever spoke about.”
Norris makes the claims in his new book, ‘A Kick Against the Pricks’.
He writes that a grand-nephew of Collins, also called Michael, was the landlord of the Irish Gay Rights Movement’s first headquarters in Dublin’s Parnell Square.
He claims it was this Michael Collins who told him that the Irish revolutionary leader was gay.
Norris writes: “I had a chat with him in the coffee bar and was greatly amused to hear that, according to him, he shared this trait with his great-uncle.
“I don’t know if he was teasing or not but a subsequent event appeared to confirm it.
“An elderly man came in one night who had been visiting Sinn Fein’s headquarters three doors down.
“He had fought in the Civil War more than half a century before and claimed to have been one of Michael Collins’s principal boyfriends.
Norris adds: “I mentioned this to a well-known popular historian of the period, who confirmed that this was generally known in certain republican circles.”
Grand-niece Owen however has confirmed that she had a number of first cousins called Michael Collins but said: “I don’t know what grand-nephew that is that Mr Norris is referring to. I know nothing about that conversation so I can’t confirm it or deny it.
“I am bemused by Mr Norris’s claim, I don’t know how much David Norris was able to check it out.”
She did admit that contemporary accounts of Collins wrestling male friends to the ground – horseplay as she put it - may have contributed to rumours that he was gay.
But she also pointed out to the Irish Independent that there was evidence that he was popular with women . She said: “He was engaged and had a girlfriend.”
The Sunday Times newspaper reports that a number of high-profile historians have also dismissed the Norris claim.
UCD professor of modern history Diarmuid Ferriter suggested: “It is wishful thinking on David’s part.
“I’ve never seen any kind of proof that Collins was ever sexually active. I believe he died a virgin.”