And the rumours have prompted plenty of reaction from fans on Twitter.
Liverpool supporters have made their stance clear: they'd love to see Benteke leave but are deeply unimpressed by claims the Hammers don't want to pay the 25-year-old's full wages.
These are only rumours, of course, and that may not be the case at all for West Ham. If it is, though, Reds fans would object.
Opinion among West Ham fans is more mixed, meanwhile. Several are excited by the idea of Benteke moving to the Olympic Stadium. His goalscoring credentials were proven at Aston Villa and he is a powerhouse in the air.
Others don't want a Liverpool 'reject,' however, and feel there are far better options on the market.
Here's a selection of how both Hammers and Reds fans have reacted to the Benteke rumours on Twitter:
The fume Benteke generated after the Palace match was worth £12.5 million, so I'd definitely accept £20 Mil for him if WHU want him.— Sam McGuire (@SamMcGuire90) March 15, 2016
Benteke needed at WHU next season. Not a Klopp type of striker but would score 20+ for us every season if fit imo.— Cheikhou (@Kooyate) March 15, 2016
If West Ham want Benteke, pay his wages in full or jog on, LFC shouldn't have to contribute to his wages should he leave— Martin (@Martin_Rich_91) March 16, 2016
According to reports West Ham want Benteke but want us to help them pay his wages? Poverty club lol.— Keri (@KeriAnnGregory) March 16, 2016