The two sides contested one of the games of the season at Anfield on Sunday, with the Reds emerging victorious when Jordan Henderson sealed a 4-3 success with his second of the afternoon.
Rodgers' previous employers can feel aggrieved not to have taken anything other than pride from the game, having fought back from two early goals to level at 2-2 and 3-3.
The away performance spoke well of Monk's impact since being appointed caretaker manager earlier this month, when the club sacked Rodgers' successor Michael Laudrup.
Having been on the Swans playing staff for 10 years before moving to the dugout, nobody knows the club better than Monk and Rodgers sees him as the ideal man to take the reins on a permanent basis.
"He's absolutely first-class," said the Liverpool boss.
"He's a good man and he'll be up early in the morning until late at night trying to make Swansea successful.
"He's been thrown in at the deep end with no experience and how he's dealt with that has been fantastic.
"He's really calm and you can see the players working for him
"They had a wonderful spell with Michael in charge but they decided to make the change and Garry is a guy who can really carry the club forward.
"He's done exeptionally well so far and I hope he gets the continued chance to build his career as a manager because he's a good man."
As for his own club, results at the weekend left Liverpool six points clear of Tottenham in fourth place and just four off table-toppers Chelsea.
They remain outsiders for a title tilt, largely due to their erratic defending, and Rodgers accepts cooler heads may be required in the run-in.
"I will want us to show more calmness at times," he said.
"You have to have solidity and we were nervy from behind. That's something we need to be much better at.
"But I think in the big games we've been at our best this season - Tottenham, Arsenal, Everton - and we've got some of them still to come here."
Monk but could hardly hide his excitement when he spoke about the future of the team.
Having lost some of their spark in the final days of the Laudrup administration, there is optimism once again at the Liberty Stadium and Monk shares it.
"To be at Liverpool pushing for a result until the last second after drawing with Napoli (in midweek) fills me with confidence and it should fill the players with confidence too," he said.
"We've only been working with them two weeks and if we can go forward even longer the sky's the limit.
"That's what they have to believe and that's what I have to believe. It's why you do it."
Monk also dampened speculation that star striker Michu, currently out injured, could be heading to Russia before the country's transfer deadline.
"Michu is the type of player who will attract interest and he is a good player, but he needs to get himself fit and that's got to be his first priority," he said.
"We're not a selling club."