Capello's England contract expires after Euro 2012 and Redknapp is seen as the most likely choice of successor by the Football Association.
FA chairman David Bernstein has previously said there was "a national desire" for the next England manager to be English and Redknapp's success, especially with Spurs in recent years, makes him the outstanding domestic candidate.
Bernstein, who was meeting Capello for talks over the Italian's public criticism of the FA's decision to strip John Terry of the England captaincy, has not ruled out another foreign coach - and Jose Mourinho would be another leading candidate - but said the preference would be for an English manager.
Bernstein said last year: "I would prefer to see the best manager possible managing the England team.
"If he was English that would be preferable for obvious reasons and I think there is a national desire for that."
There would be contractual issues with Tottenham to sort out if the FA do want Redknapp to take over the national team ahead of the qualifying campaign for the 2014 World Cup, which kicks off in September.
Bookmakers Ladbrokes cut the odds on Redknapp being the next England manager from 2-1 to 1-3 within seconds of the acquittal by a jury at Southwark Crown Court, before then suspending betting altogether.
The bookies are still taking bets on England winning the 2014 World Cup in Brazil under Redknapp. Alex Donohue of Ladbrokes said: "As soon as the verdict was known punters got stuck into Harry for England. If he does the business in Brazil it will cost us millions."