Mina signed for Everton late on deadline day, after a summer of speculation over his future.
United had initially come in for the Barcelona defender, but baulked at the agent fees involved in any transfer.
Everton, though, managed to get a deal over the line, and the Red Devils are concerned that the transfer could distort the market.
United were criticised for a lack of action in the transfer window, but they are still privately hoping that Everton simply managed to negotiate the deal down to a cheaper price than they were able to.
Jose Mourinho’s side are fearful that if Everton paid what Mina’s agents were wanting, then the costs for agents fees across the board will rise in future.
Mina was one of three signings that Everton made on deadline day, with Bernard and Andre Gomes also arriving.