Redknapp was thought to be the front runner to replace Fabio Capello in charge of England last year, but the Football Association opted to offer the job to Roy Hodgson instead of the then-Tottenham Hotspur manager.
The 66-year-old revealed that he had approached Rodgers, who was then in charge of Swansea City, during a match between Spurs and the Swans and that the Northern Irishman had agreed to become his number two.
"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 [Ferdinand] and [John] Terry or [Wayne] Rooney and [Steven] Gerrard?" Redknapp wrote in his autobiography, which is being serialised by the Daily Mail.
"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.
"Some Tottenham fans might think I was distracted from my club job, but I can assure you the conversation took five minutes. And we beat Swansea 3-1 that day, by the way. It didn't work out. On April 1, I was contemplating the way forward for England with Brendan Rodgers - and on April 29 the FA offered the job to Roy Hodgson."