However, Rodgers has insisted that the discussions between him and Redknapp never reached that stage.
"My version was that April when I was manager at Swansea, Harry had asked me after the game when we played," Rodgers told ITV Sport. "He pulled me aside and it was a unique conversation because he was obviously very confident - as was the nation - he was going to be offered the national team job.
"Here was a Premier League manager asking another Premier League manager to come and work with him at the European Championships. It was a quick conversation. I was aware he was very keen for me to team up with him if he was given the role.
"There was no decision either way. Out of the respect I have for Harry I was going to consider it."
Redknapp is now manager of Queens Park Rangers.