The Reds skipper still has 12 months left to run on his current deal, but Rodgers is eager to tie him to terms which would allow the talismanic midfielder to see out his career at Anfield.
He claims Gerrard still has 'a lot more to give' and feels Liverpool should be looking to reward a man who has given loyal service to the club throughout a distinguished 15-year career.
Rodgers said: "Steven has a year left and that is something he and I are about to discuss.
"Then, I will take things through to the board upstairs.
"There is no doubt that Steven is a player who has given so much to the club, but he has also got a lot more to give.
"It just emphasises how selfless Steven is that he hasn't wanted to talk about a contract because his focus has been on the team and improving his own game.
"But, obviously, I want him to know that he is very much a part of what we are doing here and a new contract is something we will look at between now and the summer."
Rodgers added: "Steven is in the same category as (Ryan) Giggs purely because of his professionalism.
"Players that go beyond a certain age have looked after themselves since they were 19 or 20. It's not by accident.
"These players sleep and rest in the afternoons. They eat the right things and keep their bodyweight the same. When it comes to the point when other players get injured and can't go on, they keep playing because they've looked after themselves.
"That is down to professionalism and commitment to their profession. Steven comes in every single day at the same time. He's like clockwork. He gets in early, lets the medics assess him, eats the right foods and is ready to train at 10.30am.
"I have never seen him give less than 150 per cent. He never has a lazy day.
"Steven is an incredible player and I have never even thought about replacing him because he has many more years left in him."