The Mali international made 37 appearances in all competitions for Lens during the 2021/22 season, scoring once and laying on four assists.
The Eagles have been pursuing the 22-year-old ever since the season ended and had tabled an offer of around £15m, which was quickly rebuffed.
After further negotiations, the Eagles have put forward a new offer of £18m upfront with £5m in add-ons, with Lens appearing ready to accept.
Though the clubs are yet to finalise the deal, Patrick Vieira’s side believe that agreeing upon personal terms will not be an issue as Doucoure has his heart set on a move to the Premier League.
Lens finished the Ligue 1 season in seventh place, with some standout results along the way such as beating Marseille and Monaco away and twice avoiding defeat to current champions Paris Saint-Germain.
The Eagles are in need of midfield reinforcements amid the departure of loanee Conor Gallagher to his parent club Chelsea.
Crystal Palace finished the Premier League season in 12th place as the only team in the bottom half of the table to register a positive goal difference.
