Rodgers led the Reds to within touching distance of their first league title for 24 years last term and won the LMA Manger of the Year for his performances, and the former Leeds United boss thinks that the Northern Irishman would be the ideal coach for the Three Lions.
The Daily Mail quotes him as saying: "[Rodgers] changed Liverpool around. He went in there and knew how they wanted to play straight away, got Andy Carroll out and got them playing.
"I think if you look at Brendan Rodgers at Liverpool and Roberto Martinez at Everton. They won't leave, but [the FA should] give somebody like that a five-year contract and say 'go with the kids'.
"And on the international scene it's got to be like that. His major problem is if Luis Suarez is now swallowed up by Real Madrid or Barcelona, because if he is, Liverpool will not be anywhere near the same team."
Rodgers joined Liverpool from Swansea City in 2012.