The Reds skipper hinted that his future may lie elsewhere if he is not offered fresh terms when his deal ends next year earlier this week.
However, Rodgers told BT Sport that talks have begun between the club and Gerrard's representatives.
Rodgers said: "I've spoken with Steven's representative over a week ago, so a real productive good conversation. We took that to the ownership and they are obviously now in the process of getting a deal hopefully agreed and done.
"I very much want him to be a part of what we are doing here. He's been a brilliant captain for me. I relayed that to the ownership.
"I'm sure he will go away with that and hopefully his representative will organise a deal. Steven is very much part of what I'm doing here. He's a unique player, a unique talent."
Liverpool were beaten 1-0 by Newcastle United on Saturday.