The midfielder left Portugal for Old Trafford in January in a £47 million deal.
Sampdoria, who sold Fernandes to Sporting in 2017, claim they are owed around £4m by way of a 10% sell-on clause -- so far unpaid -- prompting the Italian side to ask the governing body to launch a probe.
There is no indication United are liable for any of the money.
A FIFA spokesperson said: "We can confirm that on April 3, 2020 the Italian club, UC Sampdoria, lodged a claim with FIFA against the Portuguese club, Sporting Clube de Portugal, related to financial obligations set out in the contract corresponding to the transfer of the Portuguese player, Bruno Miguel Borges Fernandes.
"The matter is currently being investigated and consequently we cannot provide further comments."
Fernandes spent one season at Sampdoria before joining Sporting for £7.5m in 2017.
After scoring 64 goals in 137 games in Lisbon, the 25-year-old moved to United for an initial £47m, although the deal could end up costing more than £67m if a series of clauses are met.
Sampdoria believe they are owed 10% of any profit made by Sporting on Fernandes.
Sources have told ESPN that Sporting deny the claim and believe they are innocent of any wrongdoing.