Afobe was snapped up from Wolves in a £12 million deal but he has struggled to hit it off with the Cherries, who are looking to recoup as much cash as possible when the window re-opens.
Wolves have the money and are keen to take him back after he scored 23 goals in 48 appearances for them to make him one of the most prolific goalscorers in the Championship before heading to Bournemouth.
Afobe has struggled for goals and fitness and has slipped down the pecking order following the arrival of Jermaine Defoe, and reports claim Bournemouth will sell if they receive a big enough offer.
Wolves are leading the chase, but there is also interest from Albion, who could pip their arch rivals to a deal by offering Afobe the chance to stay in the Premier League.
The Baggies enquired about his availability in the summer and could make another move in the new year.