The Baggies have targeted the wideman after his impressive displays this season led unfashionable Pacos to third place in the Superliga and a chance to qualify for the Champions League.
Hurtado has six caps for Peru and was included in their squad for the World Cup qualifiers in March, which gives him a good chance of obtaining a work permit to play in the UK.
The former Alianza Lima star, 22, is nicknamed 'horse' back in his home country where he has just arrived to begin preparations for Peru's next qualifiers against Ecuador and Colombia.
Hurtado is also selected for Peru's friendly against Panama on June 1 but could miss it with a slight injury niggle.
WBA face serious competition from Sunderland for the winger's signature with the Black Cats already having established contacts in Peru.