Allardyce replaced Paul Ince as Blackburn boss earlier this week.
“If the call came from England in a few years then that would be great,” Allardyce told The People.
“But I would have to be sitting as a top Premier League manager at this club at that particular time for me to be considered.
“Managing your country is the pinnacle for any manager and I’m no different.
“One day I’d love to do it. But if it’s not me then we have still got to get an English manager – and that’s no disrespect to Fabio Capello, of course.
“I’m an Englishman and purely from a selfish point of view I want to see an English manager in charge of the England team because we have enough good home-grown coaches with a great knowledge of the game.
“I want to see British managers managing more of the top-four teams in the Premier League and I hope it can happen.”
