The reported claims that the Hammers are considering making a late bid as they continue efforts to sign a new striker.
The East London based outfit suffered an injury blow to summer signing Andre Ayew who had to be taken off injured.
The Hammers could face competition from Besiktas who have offered to cover £3.91 million or Benteke’s wages to sign the Liverpool striker on loan.
Black Eagles vice-president Ahmet Nur Cebi has confirmed that the club want Benteke on loan.
“Benteke is a player we are interested, we are pushing for him and would want him to be transferred to the club.” Cebi revealed to Turkish-Football.
Crystal Palace have also been in talks with Liverpool over Benteke but the Reds want £32 million for the Belgium international according to the Mirror.
Liverpool want to sell Benteke and head coach Jurgen Klopp has made it clear he has no plans for him next season after dropping him from the team that beat Arsenal 4-3.