Van Persie has been linked with the likes of Real Madrid and Barcelona and has just over a year left on his current contract with the Gunners.
The striker is set for new talks with Arsenal about his future at the end of the season.
“I do not see Van Persie leaving Arsenal,” Arteta told COM Radio.
“He is completely unaffected by interest from Real Madrid and Barcelona and not thinking about his contract renewal either.
“Now he is very calm and is not nervous about anything.
“I know he has said that in the summer he will consider things, talk it over and take the decision that he will take.”