Gerrard believes the FA must appoint the best person for the job, even if they're not English, but praised Redknapp for the job he has done at White Hart Lane and said the 64-year-old was a serious contender to take control of the national team.
"For me it has to be the best manager, but I also do agree that there are very good English managers out there," the England midfielder told Sky Sports. "Harry Redknapp's name crops up a lot and I don't think he gets the credit he deserves for what he's done at Tottenham and there's also maybe two or three other candidates along with Harry.
"I don't see why we should have to look abroad if the English managers are good enough to do it and I believe they are, but for me it's always a case of pick the best manager that can bring success for the country."
Liverpool captain Gerrard also thinks Wayne Rooney must be included in the squad for the European Championships even though the Manchester United striker is suspended for the first three matches, following his red card in England's final qualifier against Montenegro.
"It's a no brainer for me," Gerrard said. "He's our best player and he can produce the goods if we're to get out of the group and go further into the competition. It's a massive blow for everyone in England that Wayne's missing but we have to accept that now."