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Wilshere, 25, left Arsenal last season to join Bournemouth on a season-long loan in search of regular first-team action.
He fell down the pecking order following the £35million arrival of Granit Xhaka from Borussia Monchengladbach.
The England international made 29 Premier League appearances for the Cherries, but his progress was cut short by a fractured leg he suffered in April.
Wilshere has since returned to Arsenal, but doubt has been cast over his future with just 12 months remaining on his contract at the Emirates.
Serie A side Sampdoria have apparently shown an interest in the midfielder.
And it is claimed that Arsenal are prepared to offload him for just £8.9m.
But Arsene Wenger is confident Wilshere will stay at Arsenal for the forthcoming season.
However, he has warned him that he must fight for his place once he fully recovers from his injury.
“When he returns, he won’t be far from practising with the team,” Wenger said.
“He has to work hard to come back and fight for a place in the team.”
He added: “I think Jack will be with Arsenal next season, yes.”