"We will write to FIFA and the Serbian federation asking for damages to the value of several million euros," Constantin told the newspaper Nouvelliste.
"It's necessary to solve this problem where we are obliged to put players at the service of national teams and receive no damages when they return to the club with serious injuries."
Sion said on their website that the 27-year-old had injured his right knee during the 2-0 defeat in Queretaro after coming on as a substitute and would be out of action for several months.
The European Club Association (ECA) said last year that it wanted FIFA to introduce an insurance policy to compensate clubs in such cases.
Sion are involved in a complex legal battle with European football's governing body UEFA over their exclusion from the Europa League, having defied UEFA and FIFA statutes by taking the case to a civil court.
Sion were kicked out of the competition for fielding ineligible players in a qualifying tie against Celtic.
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