He has offers from across Europe to continue playing and he has also held talks with his former Anfield club about a coaching role.
Rodgers, who worked with Gerrard for three years at the Merseyside outfit, has played down the possibility of him moving to Parkhead.
He said: “There is obviously some speculation. I would never say anything about what we would be doing business wise anyway, but I think there is probably a natural focus on him because he is leaving and there is a period now where he can go to another club.
“We worked well together in our time at Liverpool and I have brought players here that I worked with before, so people see it as a natural progression. But there is nothing in it.
“We’ve kept in touch. Obviously, with the time difference recently, it’s been a bit less. There have been text messages.
“He was old school that way. He was brought up in the history of Liverpool, where the manager is the manager.
“On that first day, he offered his support. He and Jamie Carragher, who were Liverpool guys and always will be, they wanted what was best for the club and the manager. Both of them were brilliant for me.
“They were icons of not only Liverpool, but the Premier League. They gave me great support and it meant a lot. Stevie was instrumental in what I was trying to do for the identity of the team.
“He knocked on my door and said as the captain of Liverpool he would be 100 per cent behind me. He was 150 per cent behind me, he was incredible in my time there.
“But, of course, I’m trying to build something here that’s based around the team – a dynamic team, an aggressive team and we will be looking at some targets for January.”
