Capello resigned on Wednesday night and Redknapp is currently favourite to succeed the Italian.
When asked if Redknapp would be his favourite for the England job, O’Neill said: “Yes, he would be.
“I think when Fabio was going to leave this summertime after the Euros anyway, that Harry would be favourite to take over.
“I think he should be and I think he deserves that opportunity as well. He should be the one.
“There has been a cry-out for an English manager now. His achievements at Tottenham in the last couple of years have been outstanding.
“He has got them through to the Champions League and they look as if they are going to get there again.
“He’s done exceptionally well, and with the result today in the court case, that’s no longer hanging over him and that will be a great relief to him.”
