The 25-year-old is travelling to London to have a medical and finalise terms.
Benteke, who joined the Reds for £32.5m in July 2015, would be Palace's record signing, with the deal potentially rising above £30m with add-ons.
Winger Andros Townsend was the Eagles' previous record signing, having joined from Tottenham for £13m in July.
Palace had an offer worth £23m up front, plus £7m add-ons, for Benteke rejected on Tuesday.
Crystal Palace have reached an agreement with Liverpool to sign Belgium striker Christian Benteke for an initial £27m fee.