According to the BBC, the club have tabled a £23m ($29.6m) offer for a player who has failed to make the grade in English football since arriving from FC Porto in a costly £32m deal in 2014, making only 64 appearances and spending a season on loan at Valencia. However, it is said that Mangala is not keen on a switch to south London as he eyes a possible move to Inter Milan.
Palace have retained an interest in 2016-17 player of the year nominee Sakho throughout the summer after his impressive exploits during an injury-curtailed loan spell at Selhurst Park in the second half of last term provided the catalyst for the Eagles' escape from relegation.
Sam Allardyce and managerial successor Frank de Boer have each been eager to secure the permanent signing of the 27-year-old, who has not played for Liverpool since April 2016 after falling out with Jurgen Klopp and being sent home from last summer's pre-season tour of the United States. However, both warned that the deal would likely be too expensive for Palace to afford.
De Boer signed Jairo Riedewald from former club Ajax earlier this summer and also recruited Timothy Fosu-Mensah on loan from Manchester United as he tries to instigate a major tactical switch. However, a wretched start to the new campaign - in which Palace have failed to win any of their opening three Premier League matches, conceding six goals and scoring none - has placed the new boss under significant early pressure and also highlighted a desperate need for further defensive reinforcements.
It was reported earlier this week that Palace had failed with a third offer for Sakho that included £22m up front and potentially a further £3m in add-ons, although there still appeared to be a great deal of confidence that they could get the deal over the line before Thursday night's (31 August) 23.00 BST deadline. However, it seems that Liverpool's refusal to budge on their well-documented £30m asking price may scupper their chances.
Southampton, West Ham United, AS Roma and Napoli have all been credited with an interest in Sakho at various stages of the current window, with Klopp seemingly not willing to alter his stance on the French international despite his current defensive options being subject to criticism and a deal for Virgil van Dijk looking increasingly unlikely.
West Bromwich Albion are also said to have seen an offer for Sakho rebuffed as they prepare for life without Jonny Evans, who continues to be heavily linked with Manchester City, Arsenal and Leicester City. To make things even more complicated, they are now believed to want Mangala as a replacement for their influential captain.
Leicester, who are also in the running for Evans, are additionally said to have made an enquiry for Sakho on Tuesday.