Keane has also been linked with the position, but after dismissing his own interest, the former Manchester United midfielder has insisted that O'Neill would be a "very, very good choice".
The 42-year-old told the Irish Independent: "I have not thought about it too much. I have more important things to be worried about.
"A lot of managers have been linked with it. A lot of good managers. I don't know about the favourites. I know a little bit about Martin O'Neill and I think that Martin would be a very, very good choice."