The 54-year-old last managed his country in 1998 - losing his job after comments made in a newspaper interview - and has not coached a side since leaving Wolves in 2006.
But, with no-one installed as England boss for the summer tournament following Fabio Capello`s departure, Hoddle has confirmed his interest, admitting he has unfinished business.
Referring to his previous stint in charge, he told the Independent: "If I were to die tomorrow, my life would be incomplete."
He added: "Would I get that opportunity to manage England again? 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."
Hoddle, who won 53 caps for England as a player, does not think that using a caretaker coach is too bad an idea, should Redknapp not take the job on a permanent basis, citing the example of England`s rugby union side and their temporary boss, Stuart Lancaster.
"Look at how a caretaker has worked for the England rugby team in the 6 Nations, they've done fantastically," he added.
"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. If Harry goes and does well, fine."