Wilshere has been a free agent since leaving Bournemouth at the end of last season.
Ex-England midfielder Wilshere has been offered the chance to train with the Gunners by boss Mikel Arteta, but he's yet to have made a decision on whether to do so or not.
The New South Wales outfit are understood to have held discussions with Wilshere's advisor Neil Fewings.
Jets officials are said to be prepared to spend big money to fund a title challenge under their new coach Arthur Papas.
The club has a history of making high-profile signings, previously recruiting the likes of Emile Heskey and Francis Jeffers.
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