WalesOnline says Wolves were favourites to sign the out-of-sorts frontman due to his agent being Jorge Mendes, a man who has brought many big-name players to Molineux in the past few months.
But Swansea have stolen a march on the Championship club.
The Portuguese connection between Silva and Swans boss Carlos Carvalhal could help the Liberty club's cause.
Silva hasn't settled in Italy and has failed to find the back of the net in Serie A action for Milan this season.
The former Porto striker cost the San Siro club €38 million just last summer.