Wilshere's future at Arsenal is currently in limbo, with just 18 months on his contract remaining.
The England international is spending the current campaign on loan at Bournemouth.
But, despite impressing at Dean Court, the 25-year-old reportedly faces the prospect of becoming a free agent.
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Jack Wilshere is spending the season on loan at Bournemouth
Jack Wilshere could be set to leave Arsenal
Wilshere's contract expires in 2018 but the Daily Telegraph claim neither Arsenal or Bournemouth are yet to clarify his future.
And the report also says that AC Milan are ready to bring him to Italy on a free transfer further down the line.
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Milan were backed to make a move for Wilshere last month.
AC Milan boss Vincenzo Montella wants to sign Jack Wilshere
However, a deal failed to materialise and the Serie A giants are instead monitoring his situation ahead of a future switch.
As well as Milan, Roma are also interested in luring him away from the Premier League.
Luciano Spaletti's side are in second in the league table – seven points behind leaders Juventus – and could sign Wilshere to bolster their hopes of winning the title next season.