Mr Norris made the claims in his new autobiography 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.
But Ms Owen questioned whether Mr Norris had checked that his claim was correct and said she didn't know which grand-nephew of Mr Collins had provided Mr Norris with his information.
She said that it didn't matter whether Collins was gay or not but that Mr Norris's claims were "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."
She 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."
Mr Norris made the claims in his new book, 'A Kick Against the Pricks'.
He wrote 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 said that it was this Michael Collins that told him that the Irish revolutionary leader was gay.
According to Mr Norris: "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.
Mr Norris added: "I mentioned this to a well-known popular historian of the period, who confirmed that this was generally known in certain republican circles."
Ms Owen 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 was referring to). I know nothing about that conversation so I can't confirm it or deny it."
She told the Irish Independent she was "bemused" by Mr Norris's claim, I don't know how much David Norris was able to check it out".
She said that contemporary accounts of Collins wrestling male friends to the ground -- or as she put it, "horseplay", may have contributed to rumours that he was gay.
But she also pointed out that there was evidence that he was popular with women "and he was engaged and had a girlfriend".
A number of high-profile historians have also dismissed Mr Norris's claim.
UCD professor of modern history Diarmuid Ferriter suggested that it was "wishful thinking on David's part".
He told the ' Sunday Times': "I've never seen any kind of proof that Collins was ever sexually active" and added: "I believe he died a virgin."
Collins's biographer Tim Pat Coogan said that he found in the course of his research that the IRA commander was "aggressively heterosexual" and that he "had several more women friends than people realised".