The League One outfit are seeking a new manager after dismissing Matt Bloomfield this week.
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The Mirror says Wilshere, 33, is a leading contender for the job at Kenilworth Road.
Wilshere left Arsenal last year to join the staff at Norwich City and finished the season as caretaker manager after Johannes Hoff Thorup's axing.
However, Wilshere left Carrow Road after being told he wouldn't be considered for the permanent job.
But the former England midfielder is now in line for a first senior post with Luton.