Swansea skipper Monk: Man Utd clash biggest in our history
Swansea have survived relegation from the league on the final day of the season in years gone by and also played in Europe.
But Monk said: "United have fantastic players and a great history, so it's the biggest game we've had in the club's history.
"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."