Pressure is continuing to build on Capello following the 4-1 defeat in the last 16 of the World Cup against Germany on Sunday.
England disappointed throughout this summer's tournament in South Africa with a 1-0 win over Slovenia the only high of a disastrous campaign.
Plenty of names have now been mentioned as possible candidates to succeed Italian Capello and Redknapp insists the next man should be English - and could be him.
He told talkSPORT: "They [the FA] have got a manager and until he's not the manager it's difficult to talk about it. But I'm English, who wouldn't want to manage England?
"There's not an Englishman - whether it's me, Roy Hodgson or Sam Allardyce - who would turn the job down because it's our country and we want to manage our country.
"No-one is ever going to turn that job down."
Swede Sven-Goran Eriksson also enjoyed little success in charge of the Three Lions and Redknapp thinks another foreign manager would show English football to be in a bad state
"Could you imagine an Englishman managing the Italian national team? It doesn't happen," he continued.
The Germans are the same, they have a German manager. We've ended up with two foreign managers. This guy [Capello] has a fantastic record at club level. But look, we've had a go with it now.
"When he finally moves on, in four years or whatever, surely there has to be a young guy or somebody in this country, surely we have to find a manager from England, an English manager.
"I'm not talking about a Scottish manager or an Irish manager, I'm talking about an English manager because this is where we're from, this is our country.
"We should be able to produce someone who can manage the England football team and let's be honest, they can't do any worse than what they've [Eriksson and Capello] done."
Redknapp was critical of England's performances at the World Cup, adding: "The players haven't performed.
"The whole package hasn't worked in this World Cup. I was England all the way and really thought it was our big chance, the best chance we've had of winning the World Cup since 1966. It's been a massive disappointment.
"We were average against the USA. We were disgusting against Algeria. We were better against Slovenia, but what a poor team they were. They'd be lucky to survive in the Championship."