The Family Fortunes host, who is married to Strictly Come Dancing presenter Tess Daly, is said to have flirted with 23-year-old model Rhian Sugden using his mobile phone and Twitter's private messaging function.
Kay's spokesman reportedly confirmed that the star had sent the messages, but insisted: "They never at any point had a physical sexual relationship."
The Sun newspaper, which first printed the allegations today, reports that Kay swapped details with Sugden after they met at a Bolton club. The tabloid said that it had seen Kay's messages but would not print them as they are "too explicit".
Kay and Daly have two young daughters together - Phoebe, 5, and Amber, who is 8 months old.
A source said: "This is the last thing Tess will want to hear. She is not one to hold back on dishing out a rollicking. It's fair to say this will go down like a lead balloon."