The Spaniard was made interim Blues boss after Roberto Di Matteo was relieved of his duties in November but the former Liverpool manager has not been a popular choice with the west London outfit's supporters.
However, Benitez insists it is just a "matter of time" before the fans are convinced and says he does not pay much attention to the discontent from the stands.
"When I accepted Chelsea's offer I did so because I believe that it's a good alternative," the 52-year-old told Spanish radio station Onda Cero.
| CHELSEA LATEST
|8/1||Chelsea are 8/1 to beat Aston Villa 3-0 with bet365
"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.
"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 that I would never manage a team like Chelsea.
"I would like to manage the national team [Spain], especially now that they are doing so well. As a coach I like the day to day [work]."
The ex-Valencia and Inter manager failed to pick up a first piece of silverware in only his eighth match at the helm of the Blues when they were beaten 1-0 by Corinthians in the Club World Cup and says the Brazilians were well prepared.
"It was the third final that I was in and I wanted to give it a lot of [focus]," he continued.
"It makes me laugh when the specialists in Spain collect videos and talk about English games and think they know the half of it. Corinthians spent 15 days there training just for the competition."
The Chelsea boss also had words of praise for Fernando Torres who has rediscovered his scoring touch under Benitez.
"Fernando worked and is working very hard," he said. "He can still improve and he knows it. We are making small changes to the team and the motivation. His principle objective has to be attacking and to be as close to the area as possible."
He then sent his wishes to Tito Vilanova, who has suffered a relapse of a tumour, adding: "Health is what appreciated and valued, it is sad news. In this case I know him and it is even sadder still. He has a strong character and he is a fighter, and that is the key."