Liverpool agreed a deal to sign the striker from Aston Villa last week after meeting the release stipulated in the Belgian???s contract.
The finer terms of the deal are thought to have been negotiated over the weekend after discussions between Liverpool chief executive Ian Ayre and Aston Villa counterpart Tom Fox.
Liverpool club doctor Andy Massey has flown back to England from the club???s pre-season tour of Australia and the Far East and will oversee Benteke???s medical at a facility in London.
Benteke???s medical could run over two days, and provided there are no issues, he is expected to become a Liverpool player in the next 48 hours in a deal which will see him become the club???s second most expensive signing ever.
The 24-year-old will not fly out to link up with Liverpool on tour and is expected to join up with team-mates Philippe Coutinho and Roberto Firmino, who return to the club???s Melwood training base on Wednesday after their participation in the Copa America.
Manager Brendan Rodgers will be acquiring a player who has a stunning record against Liverpool with Benteke scoring five times against them in their last six encounters.
Benteke, who has two years remaining on his Villa contract, has scored 49 goals in 101 appearances for the club since he joined from Genk in 2012.
Liverpool have already bought six new players, including England right-back Nathaniel Clyne at a cost of ??12.5m, and Benteke’s arrival would push their summer spending to around ??80m.