Monk was club captain at the Swans when Rodgers was in charge and has now replaced Michael Laudrup as manager himself.
"At the time, when I was there at Swansea, he was a magnificent captain for me," Rodgers said. "And in a lot of our conversations, which were very open, I said to him that he should start thinking about his coaching two to three years before finishing as a player.
"He's a bright lad, Garry," said Rodgers ahead of Sunday's big game. "He's very honest and very loyal as a captain. But he was one I could see having a future in coaching and management if he wanted to go down that route.
"It's probably come unexpectedly for him, especially going straight into the Premier League. But he's very calm and enjoying it at the moment. And the players have responded to him.
"He'll have gained respect because of his status there as a player, and he'll be looking to make a similar impact over time as a coach and manager.
"I think he's done brilliantly. He looks as if he's galvanised the group. He's a great learner, and always has been. Over the course of these coming months, he'll get better."