Goal revealed in August that the Gunners had made a £21.3 million bid for the Portugal international after originally having a £20m offer rejected.
Sporting value the player at £28m, though may be willing to drop their asking price, and Silva has confirmed that the 22-year-old midfielder is wanted by a number of Premier League clubs.
And though he wants Carvalho to concentrate on his own game, he cannot rule out a departure in January should a bid of acceptable value be tabled.
"William is a target for English teams, but I want him to play his game," he told reporters.
"He's not playing at the same level as last season because last season he was a surprise, but he's improving.
"William has many offers. Let's wait until January."
The player himself has admitted that a move to the Premier League or La Liga will happen "sooner or later", with Manchester United also credited with an interest in his services.
Carvalho will have a chance to impress his English suitors when Sporting take on Chelsea at Stamford Bridge on Wednesday as they look to reach the last 16 of the Champions League.