The Ivorian was sent off against Leeds United on Sunday for head-butting defender Ezgjan Alioski, an incident Arteta labelled as 'unacceptable'.
There has been speculation that the Gunners have had seen enough of the flashy winger.
But asked if Pepe could be moved on, Arteta replied: "No, absolutely no. It's not about that and I don't like that type of statement.
"I will give Nico my full support all the time. He knows the things he has to improve, but as well we all know his qualities.
"He has some responsibility and I have some responsibility which is to get the best out of him, get the best position for him and the best areas for him to do what he can do with the ball.
"I can't fault at all his effort and if you see any of his stats the way he is trying for the team, the way he is working, it's the best since he's been at the club.
"But there are certain aspects he can do better because he has the ability and that's where I'm going to put the pressure on him to deliver what he can do.
"But to say it's a threat for him to finish his career [at Arsenal], it's not at all like that."