Police were called in after the alleged incident in a nightclub in Dublin, according to reports.
Cowell said: “I have known Louis Walsh for 20 years and I don’t believe for a second that these allegations are true.” He said: “Like all of his close friends I will support him 100 per cent.”
The Irishman became a household name in 2004 when he became 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.
A spokeswoman for Walsh, 58, said he had not been contacted by police about the claims.
She said: “He vigorously denies all of the allegations.
“If contacted by the police he will willingly co-operate with any investigation.
“Louis categorically denies any wrongdoing and will fight to clear his name.”