Newspaper reports earlier this week suggested that the Swans players were leading a revolt against boss Laudrup, who replaced Brendan Rodgers over the summer.
The reports emerged in the wake of a poor run of form for the Welsh club, who won their first two league games of the season but are without a victory since.
Chairman Huw Jenkins released a statement on the club's official website on Thursday angrily denying reports of a player split.
Now club captain Monk has followed suit, insisting the squad and management are very much united.
"It was quite funny reading an article in the paper this 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," he said.
"The article 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.
"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."