Amadou is understood to be desperate to join the Premier League club and travelled to London from Lille via train earlier in the day in an effort to force through a move.
West Ham United were also interested in the 24-year-old, with both clubs making offers worth £16m to Lille, including a £2m loan fee.
However, Palace are understood to have included a £14m obligation to buy at the end of the season in their deal, whereas West Ham's additional £14m was an option to buy.
Sky Sports News now reports that Amadou is pleading with Lille to sanction a move away from the club, but the French outfit are refusing to lower their £18m asking price.
Reports have also suggested that Amadou is having a medical with Palace in case there is a breakthrough in negotiations before the 11pm deadline.