Benitez took over at Chelsea following the sacking of Roberto Di Matteo in November, signing a contract until the end of the season.
He has since picked up four victories from his first eight games but the Blues have been knocked out of the UEFA Champions League and lost the Club World Cup final, as well as suffering a Premier League reverse at West Ham.
Chelsea's supporters have not taken kindly to the appointment of the ex-Liverpool boss with boos ringing out at Stamford Bridge and angry chants directed at the new manager at every game of his tenure so far.
However, Benitez says that he believes that it is just a "matter of time" before he turns the fans around and refused to comment on suggestions he could replace Jose Mourinho at Real Madrid in the summer.
He told Spanish Radio station Onda Cero: "When I accepted Chelsea's offer I did so because I believe that it's a good alternative.
"My future? I know things, but I am not going to say anything about Real Madrid, because I believe that I should not. We are talking about two very high-level teams.
"I have a challenge that is trying to win and do good things, it's a matter of time in convincing many people.
"If we are successful it will be easier to convince them. I'm very calm."
The 52-year-old Spaniard continued to be the subject of negative chants from Chelsea supporters at Elland Road during Wednesday night's 5-1 win over Leeds in the Capital One Cup.
Benitez admitted: "Sometimes I don't understand the songs against me.
"I am concentrating on the game and I don't know what happens in the stands, but I have never said I would never manage a team like Chelsea."
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