The Script frontman mentored the singer during BBC One's talent show, which saw Bruce beaten in the final by Leanne Mitchell on Saturday (June 2).
Rumours that the pair were more than just colleagues reportedly arose among viewers and backroom staff at the BBC when O'Donoghue's Lithuanian model partner Irma Mali did not attend the final.
O'Donoghue also posted a photo of the pair on Twitter which showed them backstage drinking wine together.
However, sources close to the singer have dismissed the rumours, stating that he is just very supportive of his act.
"They're not having an affair - don't be ridiculous. They have great chemistry but that's just Danny being enthusiastic. He believes in Bo and they get on but that's it," a friend told The Sun.
All four Voice UK judges are reportedly facing the axe by producers for next year's second series.
