The interim Chelsea boss is expected to leave Stamford Bridge at the end of the season and has suggested he will one day take charge of the Merseyside outfit again.
But Rodgers is confident that, having elected not to pursue Benitez in the summer, he has the full backing of the Liverpool board.
"I haven't seen the statements but I've heard plenty of people talk about it," Rodgers told reporters.
"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.
|Carroll future still undecided
|33/1||Liverpool are 33/1 with Coral to finish in the top four
"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."