The Nigeria international spent last season with Liverpool, but some erratic displays for the Reds have left him no closer to Chelsea‘s first team.
Moses only moved to Stamford Bridge in 2012, but the presence of a number of experienced players limited his game time, with many of his outings coming in cup competitions.
But now the Baggies are ready to give him another chance as they step up their own transfer plans.
New boss Alan Irvine is thought to see the 23-year-old as a good option from wide, and believes that he can get back to his very best at The Hawthorns.
Chelsea are likely to sanction such a move if an arrangement can be reached regarding Moses’ wage demands, with the pacey wide-man unlikely to get many opportunities in west London next term.
West Brom are also monitoring Middlesbrough’s Albert Adomah as a back-up option.