Crystal Palace have had an improved bid in excess of £16m for Ibrahim Amadou turned down by Lille.
The club had a £16m bid for the Cameroon defender turned down earlier this month, according to Sky sources, and also held talks with Lille a year ago for the 24-year-old.
Roy Hodgson is in search of defensive reinforcements to deal with a growing list of absentees including Scott Dann, who is ruled out for the rest of the season after suffering a cruciate knee ligament injury.
Mamadou Sakho is also sidelined with a serious injury, leaving the Eagles with three fit centre-halves in James Tomkins, Martin Kelly and Damien Delaney.
Lille need to sell players in order to raise funds this month to comply with financial fair play rules.