The Eagles' initial £25 million bid was instantly rejected last week, with Liverpool looking to recoup as much of the £32.5 million they spent on the striker just 12 months ago as they can.
But Benteke, who scored 10 goals in 42 appearances at Anfield last season, could have his exit confirmed within the next few days with Palace now willing to meet the Reds' valuation with their second offer.
It is understood that the Londoners' bid will be an up-front fee of £27 million with the rest, £4.5 million, in add-ons. Although the deal is reportedly hinged in Palace's favour, the additional instalments centering around appearances and European qualification, that fee is likely to see Liverpool do business.
They would, provided the add-ons were eventually exercised, see them lose just £1 million of the fee they spent to make the 25-year-old the club's second most expensive signing ever a year ago.
The transfer seems to suit all parties, with Benteke keen on a switch to Selhurst Park as he searches for more game time than was on offer on Merseyside under Jürgen Klopp.
And with Alan Pardew's men looking for a top-class centre forward, having failed in their attempts to sign Benteke's compatriot Michy Batshuayi who instead chose to sign for their city rivals Chelsea, they appear eager to do whatever it takes to sign Benteke.
Benteke edging closer to Liverpool exit
With Benteke's openness to the move meaning personal terms are not expected to be an issue despite his high wages and the player's image rights, it seems unlikely he will remain a Reds player by the time he would be expected to return to first-team training.
The Belgium international will spend the next few weeks holidaying after his country were knocked out of Euro 2016 at the quarter-finals stage by Wales and Liverpool teammate Joe Allen.
Granted a minimum of three weeks of holidays after the Euros, Benteke seems likely the move could go ahead in the coming days although Liverpool could yet seek a greater guaranteed fee up-front.
But his career with the Reds is almost certain to end this summer, after a failed first campaign followed his pricey move from Aston Villa.
Signed under previous boss Brendan Rodgers, Benteke struggled to adjust to a different system and found game time even harder to come by after Klopp was named as the sacked Rodgers' successor in October.
Less than half of his appearances throughout the season came from the start and the signing of Sadio Mane last month has only pushed him further down the pecking order.
That leaves Daniel Sturridge, Mane, Roberto Firmino, Divock Origi and possibly even Danny Ings ahead of him going into the new season.
Benteke would follow Steve Mandanda and Andros Townsend in joining Alan Pardew's Palace in the last few weeks, as they look to mount a challenge for European football in 2016-17.
There has been no word yet on whether the incoming fee for Benteke would free up funds for Klopp to further strengthen his squad this summer, though he is still targeting a left-back and central midfielder.