Reports in the UK on Wednesday claimed Mustafi had rejected an extension offer from the Gunners as he plans to test free agency next summer.
For his part, Arteta has been delighted with the German since he took over last year and wants to continue working with him.
"Musti's completely fit to play and obviously the internal contract situations are going to be discussed internally," Arteta told reporters ahead of Thursday's clash with Dundalk.
"I've been really happy with Musti since I joined and the progress that he's made, the performances that he's made.
It's true that he has a long term injury and he's worked really hard to get back in that position where he is today and I just want him to show again the trust that we have in him and get the performances that we got in the past from him as well.
"I think they were a few cases when we joined in that position.
"What we tried to do was help the players as much as possible, encourage them to ply with confidence, try to give them the right solutions and then it's up to them to show with their performances where they are."