The Portugal U21 ace, who spent last season on-loan with Las Palmas, is available from Wolves for a fee of €20m.
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Dortmund have offered Silva a five-year contract and are set to begin talks with Wolves over his fee.
However, TMW says Silva favours a move to Roma and is hopeful of the Giallorossi making a counter proposal.
For the moment, Dortmund are rated as favourites to land the young centre-forward.