The Frenchman had a disappointing season with the Gunners after failing to break into the first team since Christmas.
While reports suggested Roma were interested in signing the striker, the 27-year-old has insisted he will “honour his contract” at the Emirates.
"I want to make my name in the Premier League,” Chamakh told Sky Sports News. "I started well last season and lost my way. However, I want to make a name for myself here.
"I've heard a lot of rumours about me leaving the Gunners, but I have a contract here. I want to honour it and make myself No.1 in my position. I am looking forward to that."
Chamakh joined the Premier League club on a free transfer from Bordeaux last summer.