According to Corriere dello Sport, the Serie A side have offered Silva, 23, a five-year contract worth €2.5 million annually.
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It’s understood that Dortmund had also agreed a deal with the striker, but Roma’ late push has turned his head, and Silva prefers a move to Italy.
Roma are yet to agree a fee with Wolves, however, with the Premier League club demanding a fee of £21.5 million for the striker.
The Italian club are hopeful of securing an initial loan with an option to buy next summer but it remains to be seen whether Wolves would be open to such a deal.