Slaven Bilic is West Brom's first choice to take over as head coach, Sky Sports News understands.
The former West Ham manager was interviewed for the role on Tuesday night and impressed Albion's bosses.
Bilic has now jumped ahead of Chris Hughton, Chris Wilder and Bruno Labbadia in the running for the job, but both sides have yet to agree on wages.
It is thought Bilic currently wants more money than Albion are willing to pay.
That issue is unlikely to be insurmountable though, with Bilic keen to get back into work in England after an ill-fated five-month stint in charge of Al-Ittihad in Saudi Arabia.
West Brom have been without a head coach since James Shan's run as caretaker boss ended with West Brom's play-off semi-final defeat to Aston Villa.
Shan took over from Darren Moore in March, after he was surprisingly dismissed with West Brom fourth in the Sky Bet Championship at the time.