Sterling, a reported Real Madrid target, is yet to sign the contract, which was tabled a month ago.
"The club has offered an incredible deal for a young player and I have spoken to Raheem a number of times and he is very happy here and I think you see that in his game," said Rodgers in the Daily Mail.
"The player is very happy and wants to continue working the way he has been.
"He has made some great strides in these last couple of years and has now got reward for that and hopefully his representatives can find agreement with the club.
"What he has been granted here is an opportunity - we see it with lots of young players - and they get rewarded for that but we are certainly not a club who are going to give out way, way above what a player is worth at a certain time in a career.
"It is not a case of giving any player, I'm not talking about Raheem here I'm talking in general, what they want.
"We want to reward our best talents as they are a big part of our future and we are confident that will all be in hand and sorted very soon."
The 20-year-old Sterling has scored 21 goals and provided as many assists in 112 appearances for the Merseysiders.