The Baggies had been expected to appointed David Wagner as their new boss but the ex-Huddersfield manager looks set to take charge of BSC Young Boys in Switzerland.
Before Wagner, former Sheffield United manager Chris Wilder was hot favourite to land the job.
Neil came very close to landing the West Bromwich job in April 2019 during his second season as PNE boss.
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It looked like the 4-1 defeat to Albion at the Hawthorns would be his last game as North End manager before taking up post there.
However, the following day he signed a new three-year contract with Preston to stay at Deepdale.
Neil, who turned 40 this week, was sacked by North End on March 21 after a downturn in results - culminating in three successive defeats.
His No.2 Frankie McAvoy took over as interim and after gathering 17 points in the last eight games of the season, was appointed head coach in May.
Albion are searching for a new manager after Sam Allardyce stepped down following the club's relegation from the Premier League.
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