However, Rodgers believes that Benitez, who won the Champions League with the Reds in 2005, has missed his chance to make a move back to the club.
"I haven't seen the statements but I've heard plenty of people talk about it," Rodgers told Sky Sports News. "Rafa had a successful time here in the period he was here and I think he will join a list of probably many managers throughout the world who would love to manage a great club - especially having been here before.
"Obviously that opportunity was there in the summer if the owners wanted to go down that route as Rafa was unemployed and not working. But they felt it best to go in a different direction and develop the club in a different way. And from that the board, players, myself and the club have all become one in looking to move forward and build success for the future. It is understandable any manager wanting to manage the club because it is truly a world-class football club. It is not a hindrance to me.
"Before I came here I had seen comments about Rafa wanting to be manager and I've seen comments while I've been here. But it doesn't affect me in my work or my job. My relationship is very strong with the players, we work very closely together on improving our football. We are very stable in terms of our board and the manager connection and we have some of the best fans in the world. It is a pleasure for me to be here at a truly remarkable club that many managers would want to manage, not just Rafael Benitez."
Benitez spent six years at Liverpool before leaving in 2010.