Wilshere has been restricted to playing in cup matches by Arsenal, and his performances so far this season have been eye catching.
West Ham are said to be considering making a move for Wilshere, with Bilic deliberating over whether or not to bring the England international to the London Stadium.
But with Palace also lurking, it could mean that West Ham are running out of time to decide whether they want Wilshere.
The England international would bring a lot of technical ability to West Ham, but his injury record is a concern.
Palace know they need an injection of quality, after what has been a disastrous campaign to date, and Roy Hodgson is said to be keen to make Wilshere his first signing of the January window.
And if West Ham continue to hesitate, it could mean that they now miss out on Wilshere, which could be a decision they live to regret if the England international fulfils his potential at Palace.