Sako is a free agent after seeing out his contract at Wolves earlier this summer and turning down the offer of a new deal at Molineux.
The former St Etienne man rejected the chance to stay at Wolves as he wanted to play in the Premier League.
However, West Brom have held a long-term interest in Sako and Baggies boss Tony Pulis has decided to push through a deal for the Mali international.
Sako was one of the stars of the Championship last season with 15 goals and 10 assists for Wolves as they just missed out on the play-offs.
The 27-year-old is set to become West Brom's second signing of the summer if he comes through his medical and agrees personal terms at the Hawthorns.