O'Neill said: "Harry has done a terrific job. He has got an eye for a player. He has proved that all his career and he has got a strong side together.
"They are strong defensively, they have got plenty of power and pace and they have a bit of guile. They've got the players capable of going away from home and soaking up pressure and being able to score.
"Their away form is phenomenal. It is Premier League title-chasing form, to have won five in a row.
"I think they have the squad, despite the fact they wouldn't be considered in normal circumstances, to make them as good a bet as anyone in terms of threatening the top four this season."
O'Neill added: "Do people take Harry seriously enough? I think so. People in the game certainly do. He has been mentioned for England. I wouldn't say he has not been taken seriously.
"Of the English managers, I think he is right to be mentioned with the England job."