Wilshere will be out of contract next summer, but the Gunners are moving quickly to offer him a new deal, according to Steve Stammers of the Sunday Mirror.
Stammers noted how "manager Arsene Wenger has held talks with the 25-year-old midfielder to assure him he has a future at the north London club."
Wenger's assurances and continued faith in Wilshere's talent have Arsenal hopeful the player will agree a new contract soon, per Stammers: "Talks about a new deal for Wilshere, whose current contract expires at the end of the season, have already started and Arsenal are hopeful an agreement will be reached by the end of the year to keep him at the club until 2022."
The chances of Wilshere inking fresh terms appear good after the 25-year-old recently indicated he wants to remain with the north London club.
The England international told Amy Lawrence of the Guardian: "Do I see myself staying? Of course I do. I have always been at Arsenal, I love this club. They have been good to me over the years; I have a great relationship with the boss."
Wenger's faith was repaid, at least in part, by Wilshere's stunning recent turn against BATE Borisov in the UEFA Europa League. He assisted the first goal and ran the match in Arsenal's 4-2 win.
ESPN FC's Mattias Karen saw this performance as an indicator of Wilshere's worth this season:
The superb display also prompted this praise from Wenger, per Arsenal's official website: "Hopefully, I just pray that he is not hampered anymore by any problems and then we will see him getting stronger and stronger. He has shown again tonight that he has not lost his football."
Wenger's note of caution is understandable when it comes to a player whose career has been derailed by injury woes since 2011. To put Wilshere's struggle to stay fit into context, Squawka Football noted how long it had been since he'd completed a full match for the Gunners:
That occurred after Wilshere started and finished Arsenal's recent 1-0 win over Doncaster Rovers in the Carabao Cup. Wenger has smartly used the cup competitions to let the midfielder build his fitness and improve his match sharpness.
A loan spell at Bournemouth last season provided the same opportunities before a cracked fibula meant yet another return to the treatment table for the gifted yet brittle schemer.
Wilshere's lengthy injury history means Wenger has to be cagey about how he integrates him back into the Arsenal first team. It's a difficult balancing act since the Gunners need him available often this season due to the paucity of midfield options in the squad.
Santi Cazorla and Francis Coquelin are injured, leaving Aaron Ramsey, Granit Xhaka and Mohamed Elneny as the only available senior options. Wenger can also rely on 21-year-old Alex Iwobi to play further forward, where Wilshere usually does his best work.
Having a fit-again and motivated Wilshere available to supplement his options would be a massive boost for Wenger.
The manager's adherence to free-flowing and attractive, attacking football demands players with the technique, vision and flair Wilshere possesses.
Those same qualities have some believing Wilshere can still be a key figure for Arsenal and the England national team. Among them, Andy Dunn of the Mirror, who recently wrote: "Unlikely as it seems, England's fortunes could yet revolve around Wenger's faith in Wilshere, a player who remains the most talented midfielder at [England manager Gareth] Southgate's disposal."
It may be too soon to rely on Wilshere at any level, given how carefully his fitness still needs to be managed. Yet, the fact Arsenal are even prepared to offer a four-year deal to a player with so lengthy an injury record speaks volumes about his core talents and Wenger's belief in the player.