The Eagles have been chasing the 22-year-old for a number of weeks ahead of the upcoming transfer window, which officially opens in England on Friday.
Palace boss Patrick Vieira is keen to strengthen his midfield following a successful first season in charge during the 2021-22 campaign, with Conor Gallagher returning to Chelsea following the end of his loan spell, and Cheikhou Kouyate's contract currently expiring at the end of June.
Doucoure, primarily utilised as a defensive midfielder for Lens, is viewed as a replacement for the latter, and featured in 34 Ligue 1 appearances last season to help his side to an impressive seventh-placed finish, missing out on European football by just four points.
Although the Mali international's time in France could soon be coming to an end, Palace's pursuit of him has stalled in recent days, according to L'Equipe, who are reporting that a transfer fee is yet to be agreed between the two clubs.
The report outlines how Doucoure is keen on a move to the Premier League, and that personal terms between the player and the club have already been agreed, but that a deal remains far from being done due to the demands of his current side.
Lens are demanding a transfer fee of around £21m according to the report, which as of yet, Palace have refused to pay, but with the Ligue 1 side having Doucoure tied down in France for another two years yet, their stance over a potential deal is a strong one.
After breaking into the Lens first team back in 2018-19, Doucoure helped his side earn promotion from Ligue 2 in the 2019-20 campaign, and has gone to make over 100 appearances for the club across all competitions during his stay so far.