Nene joined West Ham as a free agent in February on a contract which runs out at the end of the month.
The Hammers have already announced that the Brazilian winger will leave the club in the summer, but it appears that he could remain in the Premier League.
It is a surprise that the Baggies are interested in a player who is 33 years of age and is past his best.
Nene could make only eight appearances for West Ham in the Premier League in the recently concluded 2014-15 season.
In those eight matches, the former AS Monaco man had a pass accuracy of 73% and a shot accuracy of 33%, and he won two headers, two dribbles and three tackles.
Perhaps the fact that Nene is a free agent and will not cost any transfer fee is a factor in West Brom manager Tony Pulis’s interest in him.