The one-club man, who made his debut in 1998, has hinted at a possible move away from Anfield as he has no intention of retiring, but Rodgers is determined to keep him.
Speaking after Liverpool's 1-0 Premier League defeat to Newcastle United at St James' Park on Saturday, Rodgers explained the situation.
The Liverpool boss said: "It is quite straightforward. I had a meeting with Steven's representative about a week ago. I want him at the club and part of everything we are trying to do.
"I relayed that information to the ownership and I am sure they will go away with that and organise a deal with Steven's representatives."
Saturday's loss was Liverpool's fourth in the top flight this season, but Rodgers felt his side were worthy of a point.
"I did not think we deserved to lose, although we didn't do enough to win it," he said.
"We had defended well before the goal, but we made a mistake and that has cost us the game."
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