Van Persie suffered an ankle ligament injury during a friendly match for Netherlands against Italy in November and, after further tests when the player returned to London, it emerged it was a serious injury that would keep him out for the majority of the season.
After undergoing surgery, Van Persie is set to return to action in April and Wenger believes that Arsenal deserve financial compensation given the impact the injury is likely to have on the team's title challenge.
"We are working on this with our lawyers at the moment and we are definitely going for it," he said. "I expect financial compensation for the damage it can make to the championship and the salary involved. It is especially frustrating to lose your players for the rest of the season in a friendly game.
"Initially, the Dutch FA said it was a small problem and Robin called me to see if he could go and see this Serbian wonder doctor and it was okay. It was only when he came back here that we realised there was much more damage.
"In Holland, they have a fight between the national doctor and the guy that did the surgery on Robin. We just want to go for it because there are a lot of things that have not been done properly after he was injured."
A KNVB statement in response to the comments read: "We have taken note of Mr Wenger's statements in the media. At the moment KNVB have no comments on this matter. If and when Arsenal will take steps, the issue will be dealt with by specialists of both Arsenal and KNVB."
At the end of November, the KNVB released the following statement: "Directly after Robin van Persie got injured in the friendly of the Dutch national team versus Italy, the doctor of the Netherlands team diagnosed an ankle ligament problem.
"The Arsenal striker went to the hospital in Amsterdam on Sunday, where further examination (an MRI scan) confirmed the diagnosis of the medical staff of the Netherlands team - Robin van Persie had a ruptured ligament of his right ankle.
"The medical staff of the KNVB contacted Arsenal club doctor Gary O'Driscoll the same Sunday to inform him about the outcome of the investigation and to transfer the medical record regarding this injury. The scan was also handed over to the medical staff of Arsenal."
The KNVB's legal position is complex as, although there is an agreement with FIFA and UEFA to pay compensation to clubs for players injured in World Cup or European Championship finals matches, there is nothing formal in place for qualifiers or friendlies.