Louis Walsh said he is "extremely angry" about claims that he indecently assaulted a 24-year-old man.
The X Factor judge was voluntarily questioned by police on Friday following talks with his lawyers.
According to reports, officers are investigating claims against the 58-year-old talent show judge over the alleged incident in a nightclub in Dublin.
Walsh said in a statement: "It didn't happen so therefore there is no case to answer and I am extremely angry that someone is trying to tarnish my name and reputation.
"My phone has not stopped ringing with messages of support from around the world which means so much to me. I am hoping that this matter will be resolved as quickly as possible."
Walsh's spokeswoman added: "Louis would like to thank everyone for the overwhelming number of messages of support from around the world that he has received over the last 48 hours.
"He is back home in Ireland and has been co-operating fully with the Garda investigating the allegation. Louis is fully confident that this purported allegation will be resolved quickly and has taken full legal advice to vindicate his name and reputation following the outrageous publication of what are totally false inferences about him."
The star became a household name in 2004 when he was a judge on the X Factor, and is the only remaining member of the original panel.
He has managed a number of groups and performers, including boybands Boyzone and Westlife.
On Friday, X Factor supremo Simon Cowell said he supported Walsh 100%. "I have known Louis Walsh for 20 years and I don't believe for a second that these allegations are true," he told The Sun.