In his recently-published autobiography, Redknapp claimed the Northern Irishman accepted his proposal, which was made when the then Tottenham boss was favourite to succeed Fabio Capello.
Rodgers, Swansea boss at the time, said it never got as far as that but admitted he would have considered the offer.
"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.
"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 answer yes or no but I would have considered it for him. Out of the respect I have for Harry I was going to consider it.
"He is a wonderful chemist, he knows what he wants from a team, knows the types of players and knows the exciting type of football and I think he wanted someone to come and implement those ideas.