Monk was appointed as the Swans' interim player-manager earlier this month following the sacking of Michael Laudrup and will take charge of his fifth game against Rodgers' Liverpool at Anfield on Sunday.
Monk has played for Swansea in all four divisions and was club captain when Rodgers was manager of the club between 2010 and 2012.
The Liverpool boss said: "I speak a lot with the senior players whatever team I'm at and obviously at the time I was there he was a magnificent captain for me.
"In a lot of our conversations, which were very open, I said to him that I thought he should start thinking about his coaching, two to three years before he finishes playing.
"He was always a bright lad, always very honest and 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.
"Of course it's probably come unexpectedly, especially being put into the Premier League, but he's looked very calm and seems to be enjoying it.
"The players have responded to him. He'll have gained respect because of his status as a player and he'll be looking to make that similar impact over time as a coach and manager.
"He's a great learner and always has been, and I think over the course of the coming games and months he'll get better."
Monk's tenure could not have begun better with a 3-0 win over Cardiff in the south Wales derby, and since then he has overseen a draw with Stoke, defeat by Everton in the FA Cup and, on Thursday evening, a goalless draw against Napoli in the Europa League.
Swansea head into Sunday's match in 10th place but only four points above the Barclays Premier League relegation zone, with this season's battle to avoid the bottom three looking set to be one of the closest ever.
Liverpool's focus is at the other end of the table, with the Reds on course to earn a Champions League spot and only four points adrift of leaders Chelsea.
Laudrup was bitterly disappointed to have been shown the door by Swansea, and Rodgers said: "It's disappointing when any manager loses their job.
"It's a very pressurised situation in terms of the league but Swansea have had great success in terms of how they manage the club and how they want to work, and obviously they felt they needed a change.
"Garry's gone in there and been outstanding. I look at the four games and he's done very well. The Cardiff game is a massive game and he's come through that with flying colours.
"He changed the team a bit at Everton and they lost that one, and I thought they were the better team last night against Napoli.
"He's gone in and galvanised the group. He was a wonderful leader for me, very much in tune with what we wanted to do, and when I look at Swansea, I can see them getting back to that organisation, pressing the ball well, and having good positioning on the field.
"It will be a tough game for us."
Rodgers will welcome Glen Johnson back into his squad after the full-back's recovery from a month out with ankle and groin problems.
Mamadou Sakho and Lucas Leiva are both progressing well from their injuries but defender Jose Enrique, who has not played since November, has gone to the United States to see a knee specialist.
Meanwhile, Granada are considering a permanent move for Liverpool's Tiago Ilori after the Portuguese defender's impressive start to life in the Primera Division.
Ilori, 20, joined the Andalusian club in January until the end of the season and, despite making just two appearances, has impressed enough to leave sporting director Juan Carlos Cordero pondering a future transfer.
"For the experience he has he is calm, he has pace, moves the ball well. He has come in and fitted into the team very quickly," said Cordero.
"When the end of the summer comes we'll see if he is wanted by the Liverpool first team or if they want to sell or loan him.
"This is something that does not need to worry us now, it will come in due course as he continues to grow."
Liverpool signed the player for around £7million last summer with one eye on the future.