The striker has been allowed to leave the club all summer and Wolves have been working on securing him a permanent move away.
German side Dortmund are now the frontrunners to sign the 23-year-old after they made contact with his representatives and offered him a five-year contract to come to the Bundesliga.
There is currently no agreement with Wolves but talks are progressing well and are expected to accelerate this week.
Dortmund are working on a deal in the region of £17million, but Wolves are keen to recoup as much money as possible for a forward that cost them £35million in 2020, and are expected to push for a higher price that could reach £20million or more.
Negotiations are expected to continue this week over the final fee and the payment terms, as Wolves look to offload the player.
Silva has been with Wolves in pre-season and travelled with the team for their training camp in Portugal, but he has not featured in any pre-season games as he continues rehabbing from an injury.
It is understood Silva is now close to returning, but he is unlikely to feature for Wolves again as he nears an exit.
Silva only has one year left on his Wolves contract, but that does include the option to extend it by a further year.
However, that is now unlikely to be needed as the player closes in on a permanent move away this summer.