The Scottish winger impressed initially at RB Leipzig after joining from Nottingham Forest for a fee of £13m last summer, but then slipped down the pecking order and made just five league starts.
He is now on the brink of joining West Brom in a deal that could cost the Baggies up to £15m if they sign the 20-year-old on a permanent deal.
However, there is a possibility of a loan deal.
Elsewhere, West Brom's interest in Tottenham defender Kevin Wimmer has cooled as Albion Tony Pulis wants to divert his funds elsewhere.