The young prospect is a target for Liverpool and West Ham.
Carvalho, on seven goals and two assists this term, rejected an extension in November and will be a free agent when his deal expires at the end of the campaign.
Silva said: “Fab will be with us until the end of the season.
“I would like, except is not the right word, I would like to see him play for us at Fulham football club.
“I will not lie, it has been difficult for us to renew.
“Of course we are trying to do our best but it has been difficult. When you have a player of this talent and at this level last year of contract it is difficult to keep him with contract.
“Without a contract it is even worse. What I can tell you right now is that Fabio will be with us until the end of the season."
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