The 66-year-old was the favourite to succeed Fabio Capello ahead of the European championship but the FA eventually handed the prestigious role to Roy Hodgson.
Redknapp was in charge of Tottenham Hotspur at the time of the speculation, and the current Queens Park Rangers manager asked Rodgers to become his assistant if the FA made an approach.
The popular coach’s misery was compounded when Spurs sacked him in June 2012 weeks after Liverpool had lured Rodgers to Anfield from Swansea as Kenny Dalglish’s successor.
“If I had become the England manager I would have taken Brendan Rodgers as my No 2,” Redknapp wrote in his autobiography, Always Managing, which is being serialised by Daily Mail.
“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.
“Look at Brendan at Liverpool now — he still knows how he wants to play. He got rid of Andy Carroll because he wasn’t in that plan. That is how Spain operate: this is how we play and we don’t compromise.
“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?
“I told him I wanted England to play with as much technical ambition as Swansea. He was up for it.
“If I got the job, he said, he would speak to the people at Swansea to get their permission. ‘It would be a great experience for you, Brendan,’ I told him. ‘I want England to play like you play. Pass the ball, play and play and play.’”
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