The 29-year-old returned to Watford's starting line-up in last weekend's 1-1 draw with Tottenham after scoring from the bench against Manchester United in his first match back following a three-game suspension.
But Deeney's start against Spurs was only his fourth for the Hornets in the Premier League this season after failing to land a regular place under new boss Silva.
Deeney has been linked with a move away from Vicarage Road when the transfer window opens next month - with new Everton manager Sam Allardyce reported to be among his pursuers - but Silva insists the club have no interest in moving their skipper on.
"I'm sure he's happy here," Silva said. "What he did today in training was work normally and he comes here with that approach to his team-mates and all the staff.
"I want him to fight and work every day to keep his position and if he does not keep his position I expect him to work hard to win it back. That is what I expect of Troy.
"I don't want to talk about Troy, Richarlison, Stefano Okaka, Isaac Success leaving in January. In each moment we will decide what is the best for Watford.
"I don't know anything about any offers for Troy. I don't want anybody to leave in January. We only want to buy."