Arsenal are short on midfielders after allowing Ainsley Maitland-Niles to join Roma on loan for the rest of the season.
The Gunners will also be without Mohamed Elneny and Thomas Partey during January as they are competing at the Africa Cup of Nations.
Re-signing Wilshere, who is currently training with the club and doing his coaching badges, has been mooted as a possible solution.
But when asked about the prospect of that on Friday, Arteta said: “I think I was very clear with the situation with Jack and the role that he was going to have being around here and we continue the same way.”
Arsenal are, however, looking to sign a midfielder this month to bolster their ranks for the rest of the season.
“We are very, very short at the moment,” said Arteta. “But to be fair on a player, this cannot be the only argument to try to keep a player – and a player that has been developed and raised through our academy.
“[Maitland-Niles is] a player that has been patient in many moments and tried to fulfil his dream. He was very straight with me and I understood the situation and we think it’s good option.
“Obviously we are going to move and we are going to look for options, because we are very short there.”