The former Gunners midfielder has been interviewed by the Colorado Rapids for the MLS side’s vacant head coach position.
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There is a link between the scenes as the US club are owned by Kroenke Sports & Entertainment, who are the long-term owners of Arsenal.
Wilshere, 31, only retired from playing last year and has had an impressive start to his coaching career, guiding the Arsenal under-18s to the FA Youth Cup Final where they were beaten 5-1 at home by West Ham.
Asked whether Wilshere has the making of being a top-level boss, Arteta said: “Yeah but way down the line, you don’t know when that is, it could be very soon!
“He’s got the potential to do it, now he’s clear in his mind what he wants to do and the reason why he wants to do it, and I think it’s a big asset for the club to have him here.
“I’m really happy that Jack is part of the setup at Arsenal. I think he’s done really well.
“I think he was really needed around the academy and the place, and these things are going to happen when people are doing well.
“He’s going to get attraction, and then it’s going to come down to him to make the best decision for his career.”
Wilshere played 197 times for Arsenal between 2008 and 2018, scoring 14 goals and assisting a further 30.
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During his Gunners stay he also enjoyed loan stints with Bolton and Bournemouth.
After leaving the Emirates he spent two seasons with West Ham, playing just 19 times.
He finished his playing career with further spells at Bournemouth and Danish side AGF.