The former Southampton and Newcastle striker is out of contract this summer, after his deal with Rotherham expired and was not renewed.
Best scored 4 goals in 16 Championship games last season, and hasn’t played in the Premier League since the 2011-12 campaign with Newcastle.
But Tony Pulis is keen on the 29-year-old, and has invited Best to train with the Baggies as part of their pre-season preparations. Pulls is looking for a new forward after releasing Victor Anichebe and Stephan Sessegnon this summer.
They also may lose Saido Berahino, with both Crystal Palace and Stoke reportedly bidding for the youngster.
Defender Craig Dawson was tied with Berahino as the clubs 2nd top scorer in the league, behind Salomon Rondon who netted 9 times. Scoring goals was an issue for the Baggies, netting 34 from their 38 games, with only relegated Aston Villa scoring less.