The 29-year-old is currently without a club after his contract expired with Bournemouth at the end of last season, and he has briefly been training with Serie B side Como to maintain his fitness.
Arteta opened the door to Wilshere last week to allow him to train with the squad in his quest to find a new club, and the midfielder hinted that he is keen to take up the offer.
"I really enjoyed playing with him (Arteta), sharing a dressing room with him. To hear him come out and say the door is always open is nice," Wilshere told Sky Sports News.
"I think that it can only help me. As you said, being around good players, training with world-class players and, as well, just being in a team environment is something that I am interested in. I am sure that I will have a conversation with someone at the club over the next couple of days."
Wilshere made 198 appearances for the Gunners during his 10-year spell as a senior Arsenal player, after signing for their youth team from Luton Town's academy.