Capello's contract ends after the European Championships in two years' time, or earlier if England should fail to qualify, and the FA have said they will appoint an English successor to the Italian.
Tottenham boss Redknapp, who guided Spurs to the Champions League group stage for the first time this season, has long been linked with the England job and said it would be tough to resist should he be approached.
"If you're an Englishman it would be hard to turn it down. It's the pinnacle of your career," said Redknapp.
"If you've got good players, managing England wouldn't be that difficult. And we've got good players, so I'm sure somebody out there could do it," the 63-year-old added.
Blackburn Rovers manager Allardyce, who put himself forward for the England job in 2006 but lost out to Steve McClaren, is ready to go through the whole process again.
Allardyce said: "Is that for me? Well, I went for it last time, so it's obviously 'me'.
"I remember speaking to Bobby Robson and Terry Venables. They said it's the greatest job you could ever have, so you want to do it. And if you feel like you can do it, you put yourself up for it. I've done that before but came a close second.
"International management does appeal, yes. I'm 55 and a different style of management appeals."
Sunderland manager Steve Bruce has already received the endorsement of Redknapp, and is also amongst the front runners to replace Capello.
Bruce said: "Of course, I would be interested and it's very kind of Harry to mention me. I would love to have a go. Why not? It must be the proudest moment of your life, even though you know what is going to go with it.
"I agree it should go to an Englishman. I have total respect for the guy in the job. But can you think that an Englishman would be managing Italy, Spain or France?
"It's all about timing, about how I do with my team over the next 18 months. But there might be a new kid on the block by then - Ian Holloway, for example."