Wilshere is in advanced talks with Norwich City to join the senior coaching staff.
Arteta said at today's media conference ahead of tomorrow's trip to Bournemouth: "He has been great, everyone knows about his career and his character, he is a special personality. His attachments to this football club is unique, he had it.
"He has this aura, charisma and a way with connecting to people. He came here and had a real impact."
Arteta also commented on Thomas Tuchel's appointment as England coach.
He said, "I understand opinions and feelings but that is the responsibility for the FA to say 'okay, the first filter is only English managers or the filter is any manager from any country and we select the best for the moment we are in right now'. I understand it can feel sad for some people not to have an English manager there and the history tells you as well how important this could be but I think I would take a lot of pride that a lot of managers would do anything to become the English manager.
"That is related to how we are treated in this country. How much we love the passion, the respect, the history and the way things are done in this country. I can say personally, you feel so related to where you are even though you are not from here. I think that is a huge thing."