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.
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."
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!"
