O'Neill said: "We want to do it (the new contract) and Martin has been pretty receptive. I cannot say for certain about anything until people actually sign a deal.
"What is the chance of it happening? I couldn't say. We want to do it and we've been in contact.
"But this has got nothing to do with Martin Laursen proving his fitness. He has done that now. He has played consecutive games when I would have had serious doubts about it this time a year ago.
"He has proved himself worthy and I want to do it (the contract). I've got a lot of regard for a lot of our players in the dressing room and Laursen is up there with any of them."
O'Neill paid tribute to Laursen's determination to regain full fitness and his bravery in never shirking a challenge at both ends of the pitch.
He said: "Martin is a competitor. He doesn't think there are lost causes. He has been terrific. You would have got long odds on this 18 months ago and it is great credit to him and I genuinely mean that.
"He was desperately trying to get fit. He had been out a long time. Lesser people than him might have thought 'this might not be for me'.
"As for his goals, Martin is on a good run. He could go the next 25 games and not score a goal but he gets chances every game.
"This is not a case of where he is going up the pitch for show. He is not going 60-70 yards, expending energy, without wanting to do something. He is capable and wants to get in there."