With Ange Postecoglou under huge pressure at Forest this international break, the Daily Mail says Silva is the man owner Evangelos Marinakis sees as the ideal City Ground manager.
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However, any move for the Portuguese won't happen until the summer given the compensation fee likely involved.
Silva resisted an approach from Benfica over the summer to stay at Craven Cottage.
Meanwhile, Postecoglou will be speaking with Marinakis this week to consider his situation with the Australian yet to win any of his first seven games in charge.