ESPN reported earlier this week that Benzema was offered a two-year contract worth €400 million to move to Saudi Arabia in January, the same deal as Cristiano Ronaldo, who joined Al Nassr after leaving Manchester United.
Benzema, 35, has spent 14 seasons at the Bernabeu, becoming the club's second-highest goal scorer and winning five Champions Leagues, four LaLiga titles and the 2022 Ballon d'Or.
The centre-forward had been expected to stay at Madrid for one more season until June 2024 but is opting instead to accept a new challenge. Madrid are in advanced talks to sign Joselu on loan to replace Mariano Diaz, but they will look for someone else to bolster the attack.
Benzema refused to be drawn on the reports on Thursday as he received the Marca Legends award at a ceremony.
"Why do I need to talk about my future? I am at Real Madrid. Not everything that you read on the internet is reality," he said. "For the time being I'm here. I'm enjoying my time. There is a game on Saturday, and I train tomorrow."
Madrid's club captain has had an injury-hit season -- missing the 2022 World Cup in Qatar with a hamstring problem -- but still scored 18 goals in 23 LaLiga appearances, as well as four goals in the Champions League knockout stage.
Benzema joined Madrid from Lyon in 2009 as one of Europe's highest-rated young forwards. He initially had to compete with Gonzalo Higuain for a place in the side, before becoming a part of Madrid's iconic "BBC" forward line alongside Gareth Bale and Ronaldo.
Asked whether he plans to speak to the Madrid fans about his future, he said: "Speak of what? "What am I going to discuss? What is being said is from the internet, and reality is not internet."
"I was a child when I arrived at Real Madrid, I was 21 years old. I just wanted to enjoy myself and look at all that I have won. There is no other club like Real Madrid, playing at the Santiago Bernabeu, the place where the greatest of this sport have played. I'm very proud of my career."
"The road to the Champions League last year was special. I don't know if it will happen again, but it's the best road I've experienced. When I'm on the field, I feel like they [Bernabeu fans] love me.
"Football is about enjoyment, the day I go to [Madrid's training ground] Valdebebas and it feels like work, I will give it up."
With the departure of Ronaldo in 2018, Benzema evolved into the team's main goal threat. He had a career-best season in 2021-22, top scoring in LaLiga with 27 goals and scoring another 15 in the Champions League, form that won him the Ballon d'Or in October 2022.
Benzema will leave Madrid having won a total of 24 trophies: the four LaLiga titles and five Champions Leagues as well as three Copas del Rey, three Spanish Supercopas, four UEFA Super Cups and five FIFA Club World Cups. His tally of 353 Real Madrid goals -- more than club legends such as Raul Gonzalez and Alfredo di Stefano -- is surpassed by only Ronaldo, the club's career-record scorer, with 450.
Benzema retired from international football in December after France's World Cup final defeat to Argentina, having been left out of his country's squad by coach Didier Deschamps after failing to recover from injury in time for the start of the tournament.