City tackle the League Two strugglers on Sunday having enjoyed a fine start to their Premier League campaign.
Swansea, tipped as relegation favourites by some ahead of the season, are sitting a comfortable ninth in the table.
And the interruption of the cup is a welcome one for traditionalist Monk, who is relishing the journey to Prenton Park.
Speaking about the FA Cup, he said: "I love it. I've been brought up watching it since I could walk.
"It's a big tradition in this country and one of the best cup competitions in the world. It means a lot to me.
"They'll be looking to play against a Premier League side and they've got home advantage, so I'm taking it very seriously."
Monk believes, too, that his side were given perfect preparation by the New Year's Day 1-1 draw at QPR - even if he admits changes will be made.
"We have to do well, we've got a tough game," said Monk. "Tranmere will be similar to the conditions [at QPR] - tight, bobbly pitch difficult to play football on.
"I'll have to make changes because we've had so many games, but there won't be wholesale changes.
"We don't have the biggest of squads, but we have quality within the squad and I trust all of them."
Swansea will be without star striker Wilfried Bony, who is headed to the African Cup of Nations having bagged a superb last-ditch leveller at QPR.
Influential South Korea midfielder Ki Sung-yueng will also be missing as he jets off for the Asian Cup, while Jonjo Shelvey serves the second match of a four-game ban and Jefferson Montero is sidelined with a hamstring complaint.
Tranmere manager Micky Adams will be a faintly familiar face for some visiting fans, having managed Swansea for just 13 days in 1997.
And the Rovers boss is hoping to spring an upset, while also holding personal relief at a break from their league program.
He told The Daily Telegraph: "If they have an off day, we have a bit of luck and our goalkeeper has a good day then we could beat them.
"The tie has got us out of a trip to Portsmouth in the league anyway, which is good for me.
"As a former Southampton player I get all the chants down there so at least it’s delayed me from some grief!"
The teams last met in 2010, when Swansea emerged 3-1 victors in a League Cup tie.
