The 32-year-old has spent his entire career at Anfield, but his current contract expires at the end of the 2013-14 season.
But Rodgers believes his skipper still has much to offer, and is backing him to play on for many more years.
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“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 is 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 believes Gerrard's longevity and achievements at one club put him in the same bracket as Manchester United legend Ryan Giggs.
“Steven is in the same category as Giggs purely because of his professionalism," he insisted.
“Players that go beyond a certain age have looked after themselves since they were 19 or 20. It’s not by accident.”