The 66-year-old was among the leading contenders to replace former incumbent Fabio Capello following the Italian's resignation in February 2012.
But Redknapp, who was managing Tottenham at the time, was overlooked in favour of Roy Hodgson, who went on to lead England to the quarter-finals of Euro 2012.
The QPR manager questioned the FA's suitability in choosing the right candidate for the job and claimed that he had the support of senior players within the international squad.
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"How would they know? What clubs have they ever run? Who do they speak to who really knows the game?
"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 club. And they get to pick the England manager.
"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.
"But the FA went for Roy Hodgson to be the England manager - a man who is more their cup of tea."
Redknapp also revealed that he had earmarked Liverpool manager Brendan Rodgers as his assistant manager and that he had sought out the then Swansea City boss about the role.
He added: "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.
"My thinking on Brendan was this: if he can do it with players from the lower leagues at Swansea what can he do with Rio and Terry or Rooney and Gerrard?
"So when Tottenham played Swansea on April 1, 2012 I pulled Brendan after the game and said that if all the speculation about me and England was true would he consider coming to the European Championships in the summer as my part-time coach? He was up for it.
"If I got the job, he said, he would speak to the people at Swansea to get their permission."