Crystal Palace are also being credited with an interest and Wilshere will be aware he needs to be playing regularly as he attempts to force his way back into the England fold ahead of next summer's World Cup in Russian Federation.
Despite being limited to two Europa League games and the Carabao Cup so far, Wilshere has used his time on the pitch well to stake his claim for the first team. He didn't want me to play as a left-winger.
Speaking ahead of Arsenal's trip to Watford on Saturday, Wenger said: "I believe that Jack at the moment is in the best form I have seen him for a long time". He is very close to being considered like everybody else. If keeps going like he is going at the moment, he will go to the World Cup, I am sure.
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"I don't see Jack being fully fit and not going to the World Cup".
Boss Gareth Southgate warned Wilshere he has to be "playing at a good level" to return to the fray.
"If you look at the numbers after the game, I've been out for four months but I'm not the one who hasn't ran the most".
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Wilshere's main issue is fitness.
Wilshere though has not played for his country since coming on as a half-time sub during last year's disastrous European Championship defeat to Iceland. It is nearly a year since he was named in an worldwide squad. "He can open spaces and get out of tight areas".
Southgate is hardly blessed with midfield options at the moment and Wilshere is still under consideration for a place in the 23-man party that will travel to Russian Federation.
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He was linked with a loan move to Aston Villa in August and former England boss Roy Hodgson is keen to take him to Palace in January.