Redknapp was backed as a future England manager by West Brom boss Roberto di Matteo, who described him as "the obvious successor" to Capello.
"Harry is a great guy, a great manager, a football guy," said Di Matteo, whose team face Tottenham in the Premier League on Saturday.
"He has done a terrific job at Spurs and is very likeable."
Redknapp insisted that any replacement for 64-year-old Capello, who earns £6m a year to manage the national side, must be English.
"Why do the English lads waste their time doing their coaching badges and all the rest of the work if they're never going to get the chance to manage at the top level?," asked Redknapp.
"I want to see an Englishman get the job - whoever it may be - and there are lots of lads out there who could do that job, I'm sure."
Redknapp has steered Tottenham to the Champions League group stage for the first time this season, having joined the White Hart Lane outfit from Portsmouth in October 2008 when the north Londoners were bottom of the Premier League table with only two points.
He also hit out at the lack of opportunities available to English coaches.
"There are people out there in the lower divisions who could do my job, without a doubt," he stated.
I want to see an Englishman get the job - whoever it may be
Tottenham manager Harry Redknapp
"John Still at Dagenham and Redbridge could do my job. He understands the game, fantastic on the game. Never gets a chance to manage in the Premier League."
Blackburn manager Allardyce, who was interviewed for the England role after Sven-Goran Eriksson's departure in 2006 but overlooked in favour of Steve McClaren, said it was "too soon" to be thinking about applying again.
"I don't think past one week, and if I get past one month then I'm very, very lucky," Allardyce reflected.
The 55-year-old added to Redknapp's calls for Capello to be replaced by an English coach.
"I'd always like to see an Englishman succeed but the politics that are behind it is very, very difficult to overcome sometimes because it depends where you are and what you're doing at that particular time if you're English," continued Allardyce.
Capello succeeded McClaren in 2007 but was heavily criticised for the national team's disappointing performance at the 2010 World Cup finals in South Africa.
However, England are joint top of Group G after two Euro 2012 qualifying wins.
Sunderland boss Bruce is another who wants an Englishman in charge of England and would relish the chance of taking on the job.
"I very rarely blow my own trumpet but, of course, I would be interested," he said.
"I would love to have a go and why not? It would be absolutely wonderful."
He added: "You have to try to get to the top - that's what I have always strived for in whatever I've done and it's about how I do with this team over the next 18 months. It's all about timing."
Arsenal boss Arsene Wenger has previously been linked with the England managerial job.
But he said: "Let the national team take somebody from England and that represents the country. That is the best way to do it."
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