The Script frontman has been rumoured to be dating his Voice UK colleague, along with reports that he and girlfriend Irma Mali are "on a break".
However, O'Donoghue is said to have dismissed the rumours as "nonsense".
"Danny has been laughing about the rumour, saying it is complete nonsense," a friend of the singer's told The Sun.
"He says there is absolutely no truth in it whatsoever."
O'Donoghue's representative added: "He is not having an affair with Bo."
Bruce lost out to Leanne Mitchell in the final of The Voice UK on Saturday.
Watch Danny O'Donoghue and Bo Bruce sing 'Read All About It' during The Voice final below: