Hoddle, 54, managed England from 1996 until after the World Cup finals in France 1998 when he lost his job following alleged comments made in a newspaper interview, and has not managed since leaving Wolverhampton Wanderers in 2006.
In an interview with the Independent newspaper on Monday, Hoddle, who also won 53 caps for England, said he had unfinished business with national side.
"If I were to die tomorrow, my life would be incomplete," he said.
Asked if he could manage England again, he replied: "Would I get that opportunity ? Probably not.
"But I don't dwell on the past and, if we fast-forward to the present, I think we have a batch of players capable of going to the Euros and doing well. I find it a very interesting moment.
"Because Stuart Pearce, Harry Redknapp, Roy Hodgson, myself - anyone - who went to the tournament with the status of a caretaker would have the pressure off him and the players would be liberated too, not least those who have been on the fringes and are accustomed to thinking that the manager doesn't fancy them."
He gave the example of the England rugby union team who have recovered well from a disappointing World Cup under their caretaker coach Stuart Lancaster.
"Look at how a caretaker has worked for the England rugby team in the Six Nations - they've done fantastically.
"Everyone's got an edge, no one's sure of a place and everyone has an incentive. So I'd back the FA if they decided not to go for a full-time manager yet."
Tottenham Hotspur manager Harry Redknapp is widely regarded as the clear favourite to take the job full-time but the FA have also said they would make no appointment until the "back end of the season."
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