Reports this week suggested that Laudrup has lost the confidence of his senior players following their recent run of disappointing results in the Premier League.
"There are always rumours flying around every football club, but I can assure you that there is no problem here and everyone is pulling in the same direction," Monk told the South Wales Evening Post.
"It was quite funny reading an article in the paper yesterday morning saying that the senior players were ready to revolt against the manager. Well, I say funny, in fact it made most of the boys angry.
"The article [in a London newspaper] came as a surprise to us all because we are a close-knit club - always have been and always will be - whatever people say or write."
Monk added that any attempt to "unsettle" them will only make the team come closer.
"If there is a problem then everyone knows that the door to the manager's office is always open and you are listened to and treated the same whether you are a senior player or a young pro - and that's the way it should be," said the defender.
"If people want to try and unsettle us, then fine, because I can guarantee it will only make us stronger."
Swansea, who have not won a Premier League game since August 25, are currently 11th in the table with eight points from seven matches.