Wilshere, 34, took charge at Kenilworth Road in October and led the club to EFL Trophy glory in his first campaign, though Luton finished one point outside the League One play-off places and will spend another season in the third tier. He has been using his Arsenal connections to source loan talent and brought Manchester City winger Emilio Lawrence to the club in January.
Speaking to talkSPORT, the former Arsenal and England midfielder was upfront about his ambitions.
"The answer to that is yes. Whoever Mikel doesn't want, I'll just call him and ask him."
He distinguished between the two Arsenal prospects in terms of what each needs from next season.
"I think they're two different situations. Ethan's a little bit older and he's had more moments in the first team than Max. Max is still trying to find his way in there — he's still in that position of coming on and making a difference, and he needs to turn that into a start."
Dowman, 16, became the youngest scorer in Premier League history when he netted against Everton earlier this season and has made 12 senior appearances under Arteta. Arsenal are understood to be planning to keep him within the first-team environment rather than sending him on loan. Nwaneri, 18, joined Marseille in January in a loan move designed around working with Roberto De Zerbi, but the Italian departed shortly after Nwaneri's arrival and the teenager scored twice in 10 appearances under new head coach Habib Beye while seeing his game time limited.
Wilshere was philosophical about the Nwaneri experience despite the disruption.
"There are lessons to be learned on and off the pitch from a move like that, whatever the circumstances."
His links to Arsenal's loan department and academy staff at Hale End remain strong from his two years coaching the Under-18s, a tenure in which he gave Dowman his debut as a 13-year-old.
"I'm always in contact with them to see because I know a couple of them. We're always keeping eyes on them. Loans are really good at this level for both parties — for us because they add quality, but also for their development."