Sako, 30, left Crystal Palace at the end of the season and has been training with the 'Baggies' since August.
The Mali international featured 19 times for Palace in 2017-8 and scored six goals, though didn't play for the rest of the season after suffering an ankle injury in January.
He was released by the club as they decided not to renew his contract.
West Brom hope to bring in a winger as they push for Championship promotion this year.