The defender turned coach replaced Michael Laudrup earlier this month, and his former manager believes he can get the best out of the south Wales outfit despite losing at Anfield
Monk played under the Liverpool boss at Swansea, and the two came face-to-face at Anfield on Sunday with Rodgers prevailing 4-3 in an enthralling encounter.
The Swans have won just one of five matches under their new manager, and are only four points above the drop, but Rodgers is convinced Monk can guide the side to safety and is already seeing improvements.
"He's been brilliant, he's been absolutely first class," said the Liverpool boss.
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"He's been thrown in at the deep end with no experience and I think how he's dealt with it has been fantastic, really calm.
"You see the players work for him and of course over time, the real questions gets asked, 'is he a manager?' because you deal with other issues and the honeymoon period is over.
"But so far the team have been a credit to him. Garry's a guy that can really carry the club forward. I hope that he gets a continued chance to build his career as a manager."
Monk has been encouraged by his side's performances, despite losing out in the Anfield thriller, and is happy with the progress the side have made during his short tenure in charge.
"We've only been with them for two weeks in terms of what we've been trying to work on," he said.
"If we can go forward even longer than that, I think the level they can get to as a team, the sky's the limit. That's what they have to believe in, that's what you have to believe in, that's why you do it."