The Blues on Monday beat Manchester United to advance to the FA Cup semi-finals and play Rubin Kazan in the first leg of their Europa League quarter-final on Thursday in their third of six games in 16 days.
Benitez's appointment in November until the end of the season was prompted by the Champions League winners' group-stage elimination from the same tournament and a top-four Barclays Premier League place is imperative to return to the competition next term.
The Spaniard, an unpopular appointment due to his prior association with Liverpool, declined to look too far beyond winning the next game, but felt compelled to comment on his own future.
Benitez, who revealed in February he will be leaving at the end of his spell in May, said: "If we can achieve trophies and finish in the top three, fantastic. Everybody will be happy. That is my aim at the moment."
As for his own future, he added: "I like to win, to challenge for trophies. I would like to stay in a top side. A top side, why not in England?"
There has been constant speculation on a permanent Chelsea boss since Roberto Di Matteo's departure and Benitez's temporary appointment, with former boss Jose Mourinho, now at Real Madrid, continually linked.
Benitez's designs on the permanent position could be shaped by the fans' views, although their stance evident in vitriolic chanting from the stands is apparently softening following his plea to back the team after the win at Middlesbrough.
But he remains the subject for repeated criticism, with Ray Wilkins the latest to comment on Benitez's team selection.
Ashley Cole suffered a hamstring injury against Manchester United on Monday and former Chelsea captain, assistant boss and caretaker coach Wilkins believes the left-back would not have done so had he played against Southampton two days earlier.
Benitez dismissed the 'April Fools' Day' comments from Wilkins.
Benitez said: "April 1. You cannot take the comment seriously. It was April 1.
"I have a degree in sports science from Spain. It's the first time ever I've heard something like this. April 1."