Former England star Wilshere, 32, is currently in charge of Arsenal’s Under-18 squad and has been impressing.
Norwich have targeted Wilshere to replace Spaniard Narcis Pelach, who left to take charge of Stoke City last month.
The East Anglians are now talking with Arsenal about compensation to take Wilshere to Carrow Road.
Wilshere has been coaching for nearly two-and-a-half years, stepping into his first role shortly after retiring from professional football.
The 32-year-old spent most of his playing career at Arsenal, coming through the ranks at the Emirates Stadium and making 197 appearances in red and white.
Wilshere also played for Bournemouth, West Ham, Bolton Wanderers and Danish club Aarhus GF.
Sadly, the former England international’s career was severely impacted by injuries, which led to him retiring at age 30.
Wilshere, who retired in July 2022, moved into coaching just four days after hanging up his boots and was appointed as the new Under-18s boss at Arsenal.
During his first season in charge, Wilshere led his team to the FA Youth Cup final – a game in which they lost to West Ham.
This term, Arsenal are unbeaten in the Under-18s Premier League, picking up nine points from their opening five matches under Wilshere.