The Welsh club's skipper says everyone eagerly looking forward to Saturday's match at the Liberty City Stadium, and getting a result would be "the icing on the cake"
The Swans secured promotion to the top flight last season via the play-offs and have surpassed expectations with an impressive unbeaten home record, and picked up a point at Liverpool in their last outing.
The 32-year-old defender is under no illusions that their next game will be tough, but feels a positive result against United would be a crowning achievement for the Welsh side.
“United have fantastic players and a great history, so it's the biggest game we've had in the club's history," Monk told Sky Sports reporters.
"United have been champions for a record number of times now and are one of the biggest clubs in Europe and around the world. They are recognised on a par with Barcelona and Real Madrid, but they set the standard for British football.
"It's one everyone connected to the club, the players, the fans and the city are looking forward to. It will be a great occasion for everyone.
"It's something we can all be proud of and if we can get a result, it'll be the icing on the cake. But we're at home, doing well and at our best we'll give anyone a game."