Silva, 48, was asked at his pre-match press conference whether the Chelsea job changed anything about his situation.
"No. Why is it different this week? It is not at all. It is the same and the same answer that I said to you already last week. I will not make, every single week, comments about it. When something comes new, we are going to tell from ourselves, myself and the club."
Silva has been out of contract negotiations with Fulham since October, when the club presented him with a three-year offer he has yet to accept. He expressed frustration last summer at the club's failure to back him adequately in the transfer window, and that tension has persisted.
He guided Fulham to ninth last season and they are currently pushing for a top-half finish in his fifth year at the club — the longest tenure of his managerial career.
BBC Sport has confirmed he is among the candidates Chelsea are considering. The club are expected to assess between seven and ten profiles before making a permanent appointment this summer. Andoni Iraola remains the frontrunner.