Benitez's men host Dynamo Moscow in the UEFA Europa League on Thursday with the Spaniard having hinted in a recent interview that he would not necessarily be averse to a change of scenery.
But the former Valencia and Liverpool boss claims Napoli's supporters are keen for him to remain.
"Every day I meet fans who tell me they've never seen a Napoli like this, and ask me to stay," he said.
"I say that we must go forward shoulder to shoulder.
"We cannot make a projection of what will happen in the long term, but we can certainly give our best tomorrow [against Dynamo] and try to win.
"I want to win every game, both in Italy and in Europe. But what I can expect now is that tomorrow we will play an intense match and look for the best result. Then we'll see. But my future is tomorrow.
"We want to win, this is clear, but we need to show the same intensity that I've seen for most of [the draws] against Lazio and Inter."
Benitez is bidding to become the first coach to win the competition, in its various incarnations, with three different clubs.
But, while Napoli are just three rounds away from the final, Benitez maintains his side must focus on seeing off Dynamo first.
"We will play against a club that has players of international quality with [Mathieu] Valbuena, [Kevin] Kuranyi and [Aleksandr] Kokorin and is also balanced at the back," he added.
"But I have faith in my team, I want the boys to play with the mentality of always going to look for success."
