Sunderland are just one point above the relegation zone and responded to Saturday's 1-0 loss to Manchester United by sacking O'Neill.
The Black Cats will announce O'Neill's replacement as soon as possible, and the new boss will have just seven games to keep them in the Premier League.
"They must have their man lined up," said Dunn on Sunday Supplement.
"I don't understand the logic of firing someone unless they have someone else lined up. It is easy to look at it and make a case for the sacking of O'Neill. His win record is not particularly good, his signings have not done well but I don't think anyone thought he would be sacked.
"We think of him as one of the managerial greats in this country and therefore you give him a little bit longer than you usually would. We also did not think that a Premiership club in trouble would sack their manager with this limited time left in the season."
Henry Winter says that this decision was not made on one game, but does question the timing of the sacking so close to the end of the season.
"Owner Ellis Short is not an individual who would have done this suddenly," said the Telegraph man.
"He is not the type of person who has made his fortune out of knee jerk reactions. I had a chat with him before Christmas and his admiration and his respect for Martin O'Neill was very deep - as an individual and as a manager. He respected him as a friend, someone who he could have a beer with after the match and who he could see really developing the team. He would have thought deeply over this - this is not a sudden reaction to a deflected goal against the best team in the country.
"I can understand some of the logic if this had happened in the summer and I can understand the logic that Short has thought long and hard about this, but why now and who are you going to bring in now? Is it going to be a younger manager for the future like a Gus Poyet? If the alternatives are Steve McClaren, then good luck trying to impose that on the Sunderland fans. Mark Hughes as well - I think they have looked at him in the past and he is a possibility. But anyone who knows the history of Mark Hughes knows that when he joins clubs he takes a long time to impose his thoughts - for him to come in and turn them around in seven or eight games is going to be tricky."
The Sun's Shaun Custis did not see the sacking coming, but says that if you look at it from Short's point of view then it understandable why O'Neill had to go.
He said: "If you are the owner and put yourself in this position, you say that you cannot let the situation carry on - no wins in eight, we are sliding and we have a tough fixture list coming up. If you do put yourself in his position then you might understand why it is being done.
"Not many Sunderland fans are protesting about the decision - there is not a lot of campaigns to keep Marin O'Neill in the job. I feel that the view from Sunderland fans is that it has probably run its course.
"I actually thought Sunderland might survive, but watching them against Manchester United there was not a lot of creativity going on - maybe you need a new manager to give that squad a lift.
"Martin O'Neill has not been a very bouncy manager this season - one full of life and wit and having a bit of a laugh and a go at journalists which is something he used to do. It seems that the spark has gone out of him and I can sort of understand why the owner thought it was time for a change."