The Football Association says it is not in talks with three gay players about coming out following a claim from Scottish National Party MP John Nicolson on Tuesday.
Nicolson said during a Culture, Media and Sport select committee hearing with sports minister Tracey Crouch: "I understand three players are in talks with the FA about coming out and they haven't done so yet."
But the MP later confirmed to Press Association Sport that he was referring to a media report of that claim and had no personal knowledge of whether it was currently the case.
An FA spokesperson said: "We have been and are working hard so that if a player felt they wanted to have the conversation about coming out, we would be there and offer any and all the support we could.
"Ultimately it has to be an individual's personal choice."
Justin Fashanu became the first player in England to come out, in 1990, but took his own life aged 37 in 1998.
No male professional has come out while still in the English game since Fashanu, but former Germany and Aston Villa midfielder Thomas Hitzlsperger and ex-Leeds United winger Robbie Rogers did so after they finished playing in England.
During the session with Nicolson and his colleagues on the committee, Crouch was strongly critical of comments FA chairman Greg Clarke made to the same group of MPs in October.
Clarke said he "would be amazed" if there were not several gay players in England's top flight and admitted he felt "ashamed" they did not feel confident enough to reveal their sexuality publicly because of the "vile abuse" they would get back from a minority of fans.
But Crouch said she found these comments to be "incredibly disappointing" and "strange."
"We don't know if there is a player who is considering whether to come out at the moment but those comments say 'don't' and that is unhelpful," she added.
Crouch added that Clarke's comments "were not representative" of the women's game and seemed to "misjudge" the most recent research on fans' attitudes conducted by campaign group Stonewall and others.
"I would say that now has never been a better time for a player to come out, if that is what they want to do, and that is what was so disappointing about Clarke's comments," she said.
"Society's attitudes have changed to this and if there was any abuse from fans it would be tackled -- let's use all the available means to address that."