The veteran actor, who plays Ken Barlow on the ITV1 soap, discussed the rumours during an episode of Piers Morgan's Life Stories which is due to be televised next month.
Roache said of his liaison with Phoenix, who played battleaxe Elsie Tanner on Coronation Street: "It was just a one-off. It was just something that happened one night when we were together. We weren't right for each other.
"She invited me round to her flat and we had a few drinks, then one thing led to another. At that time, she had a reputation and I had a reputation, and she felt we should meet, as it were. It just happened."
Roache also claimed that he was given the nickname "C**k Roache" by the cast because of his sex drive and revealed that he cheated on first wife Anna Cropper as a result.
He initially revealed that he had slept with "more than 100" women, but when pressed as to whether the figure was closer to 1,000, he said: "Well, I'm not denying it."
Roache also discussed the fallout from his infidelity and divorce from Cropper, revealing that he started drinking after the former couple separated in 1974.
"There were plenty of girls around. I shouldn't have done it. I didn't have any control over my own sex drive. I didn't have the strength to control it," he revealed.
"It depressed me. I'm so sorry for the things that I did. The hurt was the children. I'll always regret that. Every morning I woke up regretting and hurting."
> Bill Roache: 'I won't quit Coronation Street'