Bilic has become the bookmakers favourite to take over as the next West Ham manager after Unai Emery revealed he will be staying at Sevilla.
The Hammers have also been closely linked with Rafael Benitez, David Moyes, and Carlo Ancelotti but have been unable to reach an agreement with any of the coaches in question.
West Ham are also reported to be interested in Marcelo Bielsa, Garry Monk and Michael Laudrup.
The ex Beşiktaş coach will have a two week break in Croatia before making his decision but he is expected to take over the Hammers.
The 46-year-old coach joined Beşiktaş in 2013 and resigned at the end of the 2014-15 season. The Black Eagles were unable to win silverware under Bilic but they were involved in an impressive European run this season.