In his autobiography, which is being serialised by the Daily Mail, Redknapp claims that senior players such as Steven Gerrard, Rio Ferdinand and John Terry also wanted him to take charge of the national side.
"This isn't about them giving the England job to me or Roy Hodgson, but English football being run by people who really haven't got a clue. And they get to pick the England manager," wrote Redknapp.
"Everyone said I was the people's choice, the only choice. All the senior players seemed to be up for me to get the job.
"I got quite a few text messages at the time from players saying they would love me to manage England: Steven Gerrard, Wayne Rooney, Rio Ferdinand, John Terry."
Redknapp went on to insist that he has no hard feelings towards Hodgson, who he believes was appointed because his personality is more the FA's "cup of tea".
He adds: "If I had become the England manager, I would have taken Brendan Rodgers as my number two.
"He had players at Swansea passing it like Franz Beckenbauer. You know how his teams are going to play before you kick off. They are going to pass, they are going to take risks; but England do not have that identity.
"Now we have Roy Hodgson who will keep England organised, for sure. I just hope he will also be a little bit bold, open up and try to get England playing the type of football we all want to see."
Hodgson, whose side will reach the World Cup finals if they take maximum points from their upcoming qualifiers against Montenegro and Poland, has guided England to 11 wins in 20 games so far.
The Three Lions have drawn eight matches under his stewardship and lost just once in 90 minutes.