Benteke was subject of a £31.5 million bid from Palace at the beginning of July, but with the Eagles offering only £25 million up front, they saw this rejected.
Liverpool were said to be holding out for a straight fee of £30 million, though this was not thought to be an issue.
Neither Palace or fellow suitors West Ham United are said to be willing to meet this valuation, with talks “at an impasse.”
Benteke is reported to be happy to stay and fight for his place under Jurgen Klopp at Anfield, though with Daniel Sturridge, Divock Origi, Danny Ings, Roberto Firmino and Sadio Mane all ahead of him in the attacking pecking order, this seems unlikely.
The 25-year-old is currently on holiday following the summer’s European Championship, and is unlikely to commit to a move before he returns to Merseyside, where he is due back on July 23.
A deal is thought to hinge on Liverpool lowering their demands, with Benteke’s £120,000-a-week wage also providing an obstacle in Palace’s pursuit.
It is worthwhile to note that reports from local press are still suggesting that talks are underway between the two clubs, with £30 million still the reported value.