The Script frontman is said to have had discussions with production bosses about different programme ideas, including hosting his own chatshow.
The Irish singer is being described as the "new Terry Wogan" after his profile rise since becoming a coach on The Voice UK on BBC One.
"Danny has proved a hit with the BBC1 audience. He's a very likeable guy who talks a lot of sense," a source told The Sun.
"Producers are always clamouring to find that kind of character as they draw in women viewers especially.
"He's keen to do a talkshow because, quite frankly, he loves gassing. He could easily be the new Wogan."
O'Donoghue recently said that the BBC were not expecting The Voice UK to be as successful as it turned out to be.
Watch the video for The Script's 'The Man Who Can't Be Moved' below: