A number of her party colleagues have already put their names forward as a potential leader, but the current education minister told the Irish Examiner she would also like to be considered.
Environment Minister Alan Kelly has made his leadership ambitions clear, as has junior jobs minister Jed Nash.
Limerick TD Ms O’Sullivan sees herself as a party leader, despite being only a year younger than Burton.
She said: “I wouldn’t rule myself out, put it that way.
“I hope there will be plenty of people putting their hands up, but can I stress that there isn’t a vacancy and I think that Joan is doing a really good job.”
Asked about Kelly, Nash, and Brendan Howlin, all mentioned as contenders, she said: “I think they are all really good reps. As I say, the more the better... I won’t rule myself out. For the moment, all my energies are in getting myself re-elected, but also getting the Labour voice in government. Ambition in people involved in politics is not a bad thing.”