Current national boss Fabio Capello is standing down after next summer's European Championship and Tottenham manager Harry Redknapp is the favourite to replace the Italian.
However, Allardyce is also keen to be considered for the position after being in contention for the job in 2006 when Sven-Goran Eriksson left to eventually be replaced by Steve McClaren.
Allardyce took charge at West Ham in the summer following the club's relegation from the top flight and has guided his team into fourth spot in the table after Saturday's 1-0 win over Peterborough.
He accepts he must take the Hammers back into the Premier League to have a chance of landing the England post after again outlining his determination to manage his country.
"I'd walk over burning coals to get the England job," said Allardyce.
"I am an Englishman and I want to have an opportunity like I did last time to be in the frame. The only way I can get there is by making this club great or as good as I can make it.
"And if the England job comes around and I am on top of my game as a manager because West Ham are on top of their results then my name might be put in the frame.
"Last time around I was probably enjoying the best time of my life as a manager with Bolton.
"That's why I was in the frame then. If West Ham are flying high in the Premier League, hopefully I'll be considered again. It would take West Ham being promoted."