The hosts registered the surprise result of last weekend with a 2-1 win at Old Trafford, while Sean Dyche's side was beaten 3-1 by Chelsea on Monday.
Monk's men sprung the surprise of the opening weekend, winning 2-1 at Old Trafford to ensure Louis van Gaal's reign at Manchester United began on the wrong foot.
This weekend's clash in south Wales represents an altogether different challenge, as Swansea takes on a Burnley outfit that marked its return to the Premier League with a 3-1 home defeat at the hands of Chelsea on Monday.
Many have tipped Sean Dyche's men to struggle this season, but Monk sees similarities between Burnley and the Swansea side that began life in the top flight in 2011.
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"We realize how tough it is going to be," he said. "Burnley are a hardworking side and they are a group that works for one another and are a real threat. What Sean has done is very similar to ourselves when we came up to the Premier League.
"They have kept the nucleus of their squad together and they have to believe in what they are trying to do, because this league can be very cut-throat. But if you are willing to work week in, week out then you've always got a chance."
Burnley sealed promotion as Championship runner-up playing a traditional 4-4-2 formation, with strike duo Danny Ings and Sam Vokes netting 40 league goals between them.
Vokes is currently out injured with a knee problem, with Dyche opting to partner Ings with Lukas Jutkiewicz up front against Chelsea.
Dyche has refuted claims that Burnley's four-man midfield leaves the club at a disadvantage, with most sides in the modern game opting for five in the center behind a lone striker, and the 43-year-old is unlikely to change his philosophy for this contest.
"We want to be brave in how we play," he said. "We were last season and we want to experiment with it of course. Over the season that might change slightly but we want to be brave in the early part of the season, to fathom out where we are and how we play, how that works against better opposition.
"That was my thinking behind playing two center forwards [against Chelsea], it's something I like to do. We obviously know the competition has increased, the power and ability of the opposition has increased and we want to attempt to play in that brave manner generally, but we're not naive, we might have to be flexible as the season develops."
Aside from long-term absentee Vokes, Dyche boasts a fully fit squad, and new signing Stephen Ward could be in line to feature for the first time.
For the hosts, Leon Britton, Marvin Emnes and Jay Fulton all missed the trip to Old Trafford with knee injuries and remain doubtful.