In his recently-published autobiography, QPR boss Redknapp claimed the Northern Irishman accepted his proposal, which was made last year when the then Tottenham manager was hot favourite to become Fabio Capello's successor.
However, Rodgers said it never got as far as that, although he admits he would have considered the offer.
"My version was that in April, when I was manager at Swansea, Harry had asked me after the game when we played," said Rodgers.
"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 Championship.
"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.
"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.
"There was no answer yes or no but I would have considered it for him.
"Obviously at the end of it all it was irrelevant as the job was given to Roy (Hodgson) and he has done a brilliant job.
"I was really happy at Swansea. I had spoken to them about the possibility but it was something that after the appointment was made there were no further thoughts on it.
"I saw that if it was to happen it would be a unique opportunity to show British players could play football: they are technically and tactically very strong they just need that support and confidence to go and play that way."