Everton's Ross Barkley looks set to leave Everton
With Champions League football on offer from the North Londoners, Mauricio Pochettino's interest looked to have put paid to any hopes Bilic might have had of landing a player who could step in and replace Dimitri Payet.
But news emerging this week will be encouraging for West Ham after reports Spurs are stalling over a bid.
According to Sky Sports, Tottenham are prepared to wait for Everton to lower their asking price for Barkley as the transfer window progresses.
Everton manager Ronald Koeman with Barkley
The report says Koeman's side value the 23-year-old at £50million despite the fact he only has a year left on his contract.
So with Spurs dragging their heels, Everton at risk of losing him for next to nothing next summer and West Ham flush with cash and on the hunt for three "game-changer" signings it could be the perfect window of opportunity for Bilic to pounce.
West Ham United manager Slaven Bilic and Tottenham manager Mauricio Pochettino
The Hammers have not been the same side since Payet left, lacking that true cutting edge and class which saw them enjoy a record breaking final season at the Boleyn Ground.
Barkley would be a major coup and would set the tone for the rest of what has been a quiet window so far.
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