Gunners midfielder Wilshere, 24, was farmed out on a season-long loan to Bournemouth and has yet to agree a new contract even though he has only 12 months left.
Wilshere has been recovering from a broken leg but Arsenal sent him to Dubai to complete his rehabilitation programme rather than return to his parent club for treatment.
England star Wilshere has clearly fallen down the pecking order at Arsenal under Arsene Wenger and the Frenchman staying on will not give him much hope.
Arsenal may offer Wilshere a new deal to protect his value rather than allow him to leave on a free transfer next year.
West Ham are watching developments closely while Manchester City boss Pep Guardiola is also a long term admirer.
But his recent injury record could be a concern and he would have to prove his fitness after suffering his latest setback while on loan at Bournemouth.