The Baggies are set to sign the 21-year-old on a three-year deal.
West Bromwich Albion are looking at plenty of options this summer, with one deal reportedly on the verge of completion.
They claim that a fee has already been agreed for the player and that a three-year deal is on the table for the player, with a buyback option included for Real to bring him back in the future.
They also report that his international ambitions have played a role in his decision.
Benavente was left out of the Peru squad for the Copa America this month, which would have left him feeling like regular top-class football will be necessary to become a regular for The Incas.
The 21-year-old has previously been dubbed the 'Peruvian Ronaldinho' and has been with Real Madrid since the age of eight. He also has eight caps for the senior Peruvian national team.
An attacking midfielder, it is difficult to envisage where he would play in the West Brom first-team, but when, rather than if, this deal happens it looks like West Brom will have themselves a real talent.