According to Matt Hughes in The Times, unless the midfielder is granted significantly more game time with the Gunners before the new year he will look to leave the Emirates Stadium in January, with his most likely destinations West Ham United or Crystal Palace.
Hughes added the Gunners will not allow Wilshere to leave on loan as his current contract expires next summer, while negotiations over an extended deal with Arsenal have yet to take place.
Wilshere, 25, spent last season on loan at Bournemouth and made 27 appearances for the Cherries in the Premier League, the most he has managed in a single campaign since 2010-11.
He produced some solid performances under manager Eddie Howe but hardly sparkled and, having returned to Arsenal for the 2017-18 season, he has been afforded only 37 minutes of English top-flight action in the Gunners' first seven games.
His lack of game time is not due to injury. According to Hughes, sources close to Wilshere indicate he has been fully fit since the beginning of the season.
Meanwhile, Wilshere recently revealed he has rarely been in better shape, per Squawka:
He has also shown flashes of his best form in UEFA Europa League and Carabao Cup performances in 2017-18.
It seems Arsenal manager Arsene Wenger is reluctant to play Wilshere regularly, which is not a surprise given his persistent injury concerns during his career and the fact he was away from the club last term.
Given it is a World Cup year, though, it is also no shock that Wilshere is considering his options having been moved to the fringes of the Arsenal squad.
Wenger recently said the Arsenal academy graduate could still have a future at the Emirates if he proves his fitness in the current campaign, per beIN Sports (via MailOnline's Jonathan Spencer).
A fully fit and firing Wilshere would be a huge asset for England manager Gareth Southgate.
His attacking tendencies, passing technique and dynamism mean he could offer the Three Lions something different to their current central-midfield options, Jordan Henderson and Eric Dier.
However, Southgate cannot pick Wilshere to go to Russia next summer if he has barely played in the Premier League in 2017-18.
Wilshere needs to play consistently if he is to earn a place in the World Cup squad, and if he cannot earn game time at Arsenal, he will have to look elsewhere.