QPR boss Redknapp says he has no interest in the role he was heavily tipped for two years ago - but believes the FA should be headhunting only the best managerial talent in the long term.
Indeed, at 66, Hodgson is unlikely to stay at England too far beyond Euro 2016 even if his fortunes are to drastically turn around.
And with that in mind, Redknapp sees two non-English coaches as the Three Lions' best alternatives for the job.
“It will be hard whenever Roy goes. The two brightest managers in the Premier League are both on Merseyside – one’s from Northern Ireland and the other is Spanish," the QPR boss is quoted as saying by the Daily Mirror.
“The way they play is suited to international football, the passing and movement they produce in their teams is fantastic.
“Brendan has done an amazing job at Liverpool while Martinez has been excellent this season at Everton as well.”
Both managers have unquestionably proved themselves in their roles in the city of Liverpool - but Redknapp's praise of Rodgers is particularly interesting as the Northern Irishman was once part of the 67-year-old's own England plans.
Redknapp has previously stated that his desire was always to manage the Three Lions with Rodgers behind him as his no.2. Now, though, Rodgers would be firmly set for the main job if England were ever to express an interest in the young Liverpool coach.
However, his commitment to the Anfield club suggests a role with a national side could be quite a few years away yet. Perhaps Rodgers could juggle both jobs - but the heavy demands of either would likely prove unmanageable at the same time.
Still, with so many of England's current side thriving under Rodgers' management with the Reds, the idea of the 41-year-old taking over the national team would surely be a welcome one for Three Lions fans. Only time will tell.