The French forward was strongly linked with a move to the Gunners but he remained in Madrid for the start of his seventh campaign with Real.
When asked about the rumours that he would join Arsenal, Benzema said to French TV show Telefoot: "Not at all
"I'm not going to repeat myself every time
"I'm at the best club in the world and I'm going to continue to work every year
"I'm happy where I am."
The 27-year-old scored 15 goals and set up 10 more in 29 league starts for Real in the 2014-15 campaign.
Benzema missed most of Real's pre-season due to a thigh injury but did feature in Los Blancos' 5-0 triumph against Real Betis last month.
He also played in 1-0 victory over Portugal in an international friendly on Friday and is expected to take part in Monday's friendly against Serbia in Bordeaux.
"I hadn't played for four weeks," he said
"I then played a bit with Real and I played 70 minutes with France
"I'm coming back little by little so I'm training hard to get back to my best level."
The former Lyon star is under contract with Real until June 2019.
Source : PA