Arsenal gave Wilshere, who is the Gunners' under-18 coach, their blessing to hold talks with the MLS side who are also owned by Kroenke Sports & Entertainment.
Wilshere is currently happy at Arsenal but does have ambitions to be a manager.
Other clubs in America and across Europe have the former England midfielder in their sights.
During his first season in charge of the Arsenal under-18s, Wilshere guided them to the FA Youth Cup final.
He spent ten years at Arsenal as a player, coming through the club's academy and making his senior debut in 2008.
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Wilshere went on to make 197 appearances for the Gunners, scoring 14 goals and assisting another 30.
During his time at the Gunners he had loan spells at Bolton Wanderers and Bournemouth before leaving permanently in 2018.
He switched the north of the capital for the east as he signed for West Ham, with whom he'd spend a little over two years.
Wilshere returned to Bournemouth on a short-term contract at the beginning of 2022 but was released at the end of the season.
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The 31-year-old moved to Aarhus GF in the Danish top flight, making 14 competitive appearances before announcing his retirement last summer.
Injuries would unfortunately plague his career, although Wilshere did still feature for England on 34 different occasions.
A move to Colorado Rapids would see him join a side who are bottom of the MLS Western conference.
They have won just five of their five of their 32 games thus far, with 11 being draws and 16 ending in defeat.