The 22 year-old was cleared to play for the Blades this week and was on the bench for the Carabao Cup win over Blackburn Rovers.
KVM have complained to FIFA and HLN says they're prepared to take case further.
Verrips joined the Blades on a free transfer hours before Thursday's deadline.
He terminated his contract with the club after Mechelen were removed from the Europa League following a match-fixing investigation.
But the club say Verrips "unilaterally broke his agreement".
The labor court of Mechelen, which is examining whether Verrips' breach of contract is justified, is also hearing a complaint made by the player's agent towards KVM.
It's suggested Sheffield United face having to cough up a fee to settle the matter.