After eight Premier League games, the Hornets find themselves filling one of the Champions League spots, having lost only one game to league leaders Manchester City, and they are already being tipped to be one of the season's surprise contenders for a European spot.
But the Portuguese coach, who joined Watford in the summer, has reminded his players not to get carried away as it is "too early" in the season to start thinking about competing for a place in a European competition.
Silva told reporters: "It's too early, I want everyone at the club to keep their feet on the floor and to work hard everyday to prepare the next match because in football everything changes too fast.
"I want everyone to be calm. I think it is fair we are having these conversations because we did really well in our opening eight games.
"You need to keep going, to work hard and to think of each game like it's our most important."
Watford's most impressive result of the season to date was their dramatic victory against Arsenal and Silva praised the ambition his players demonstrated after equalising against Arsene Wenger's side.
"I feel pride when I see the way they worked in the last match. I saw the ambitions we had in that moment, when we scored the 1-1 against a big team like Arsenal.
"We didn't go back, we continued with our work and tried to achieve a better result for us."
Silva will take his side to Stamford Bridge on Saturday to face Chelsea, and he insists that although the Hornets are two points ahead of last year's champions, the home team are still favourites in the game.
When asked which side is the favourite, he said: "You know the answer, no? I think you know the answer - the favourites are Chelsea of course.
"In football the last results are really important but Chelsea have players who can decide a result in one minute.