The pop star was questioned under caution last month by police as part of an inquiry into the alleged incident at a religious event in 1985. He has not been arrested or charged.
In an update on his Facebook page, he said: "This is just a brief message to thank all of you who have shown support, including those in the Press.
"I wanted to let you know that I'm doing ok and it goes without saying that I fully intend to clear my name. Just to be absolutely clear, the allegation is completely false and I will continue to cooperate with the police should they wish to speak to me again."