BBC Sport says Wilshere is the No1 choice for Luton's board after last week's dismissal of Matt Bloomfield.
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Richie Wellens is also being considered, but regarded second-choice behind Wilshere.
The former Arsenal U18 coach left for Norwich City last year and ended the season as caretaker manager.
But Wilshere left Carrow Road after learning he would not be considered for the permanent job.
Luton have suffered five defeats from their opening 11 games to leave them 11th in League One.