Sam Allardyce has made it clear he wants to sign a striker that can lead the line before the transfer window closes next Monday.
Former Leicester City striker Ahmed Musa is due to train with the Baggies this week, while Allardyce also has an interest in Galatasaray forward Mbaye Diagne.
Musa, who joined Leicester for £16million in 2016, is a free agent following his release by Saudi Arabian side Al Nassr.
Albion will run the rule over the 28-year-old in the coming days before deciding whether to offer him a short-term deal.
Benteke is another player under consideration, with the former Villa forward having enjoyed a fruitful spell under Allardyce at Selhurst Park.
It is understood Palace are willing to listen to offers for the Belgium international, who may even be allowed to leave on a free transfer this month.
But wages may prove a sticking point. Benteke currently earns more then £100,000-a-week and his demands will have to reduce significantly if he is going to complete a move to The Hawthorns.
Benteke joined Palace from Liverpool for a £32million in 2016. But he has only scored 26 goals in four years for The Eagles.
He has four this season, with two of those coming against Albion back in December.
And he has fallen further down the pecking order this month following the arrival of Jean-Philippe Mateta.
Meanwhile, the Express & Star understands Galatasaray are open to loaning out Diagne this month but not before they have signed a replacement.
The Senegal international has scored 11 goals in 18 appearances for the Turkish giants this season.
But with money tight, Galatasaray are willing to loan out the 29-year-old in the hope it puts him in the shop window for a lucrative move in the summer.
First, though, they want to sign a replacement, with Feyenoord’s Nicolai Jørgensen understood to be their primary target.