Sakho impressed in his loan spell at Selhurst Park last season and Frank de Boer has been trying to sign him on a permanent deal ever since.
The £22m plus £3m in add-ons comes in below Liverpool's valuation of the player, with the Reds holding out for £30m.
Palace have had a dreadful start to the season and are yet to pick up a point from three Premier League games.
De Boer is keen to address the weaknesses in his side and has not ruled out the possibility of new signings.
He said last weekend, "we are looking for players of course. But it has to really give quality to us. We will see.
"The club is focusing on the players that maybe we are going to get, and I am focusing on the team to get the right freshness for the Burnley game (on 10 September)."
When specifically asked about Sakho, the Dutchman added, "I don't know. We know what kind of impact he had last season. But, for now, I can't say about it."