Despite investing heavily since the return of president Florentino Perez in 2009, Madrid have remained in Barca's shadow and even the arrival of Mourinho last summer could not halt their rivals' success in La Liga and the Champions League.
However, Mourinho has already warned that his teams invariably improve after his first season and, with further additions to the squad planned before the new campaign gets underway, Benzema is in confident mood.
Asked whether Madrid could beat Barca next season, he told AS: "Sure we can. I have never doubted it.
"We are a great team, but we started last season with a new coach, with players and gradually had to fit everything together. Now we can continue with the same group and some reinforcements and I am convinced that we will be very competitive. We're going to make it very difficult for Barca, I can assure you.
"We will be very strong this year. The group is fantastic. Everyone gets along. We are very supportive and we have a very good coach. I am very optimistic about this new season."
Benzema had been linked with a move away from the Bernabeu after struggling for first-team football early on last season, but the 23-year-old seized his chance when Gonzalo Higuain suffered an injury.
Asked about the possibility of leaving Madrid, he said: "I never thought about it, even in the difficult times. That is my strength and my philosophy. I realise that when one is lucky enough to be at such an important club as Real Madrid you should be prepared for suffering. It is part of the game.
"It's easy [to explain my good form]. The coach gave me confidence and enabled me to string together several performances.
"Mourinho again put me in the side and that changed everything. I came to Madrid to score goals and provide a great spectacle of football. I want to please people. In Madrid I do what I did in Lyon, but better!"
Benzema - who had faced criticism from Mourinho - said a meeting with the coach in January was important to his revival.
He said: "I am not one who will normally go and see the coaches, but at that moment I felt the need. I asked what he thought of me and I told him what I thought.
"I calmed down. I noticed his interest and confidence. This meeting between the two of us was very important."