But which of his Preston players could Neil target this summer if he's appointed by the Baggies - and assuming the Lilywhites don't go up.
HITC Sport takes a look...
West Brom will be keen to improve upon their current full-back options whichever division they're in next season and Fisher, who was one of Neil's first signings at Preston, could be high on the 37-year-old's list after starring under him these last two campaigns.
Central midfield is another area in which Albion are likely to be busy this summer, with Gareth Barry, James Morrison, Chris Brunt and Rekeem Harper all out of contract. And signing Pearson, a former Manchester United youth, would add fresh bite to the Hawthorns' engine room. The 24-year-old's partner-in-crime, Alan Browne, would be another useful addition, but only recently signed a new long-term deal at Deepdale.
West Brom could find themselves short of wingers this summer, with Jacob Murphy and Jefferson Montero both due back at their parent clubs. And Robinson, whose Preston contract expires in little more than a year's time, may be a suitable long-term replacement, having scored or assisted 11 goals in 19 games this season. The 24-year-old has links to the Midlands, where he began his career as an Aston Villa player.