The former Lens man made a name for himself in France before joining the Eagles in last year and continued to go from strength to strength in the Premier League.
Palace shelled out €22.6m (£19.6m) to bring Doucoure to England last summer, and the Mali international immediately cemented a starting role at the base of midfield over former captain Luka Milivojevic.
Doucoure ended his debut season at Selhurst Park with three assists to show from 35 matches, starting 34 top-flight games as the Eagles finished above Chelsea in 11th spot.
The 23-year-old is under contract with Roy Hodgson's side for another four seasons, but he is believed to be on Liverpool's list of potential replacements for Fabinho.
However, the Reds risk being priced out of a move for Doucoure, as the Daily Mail claims that Palace are prepared to demand as much as £70m to let him leave this summer.
Despite his extortionate price tag, Palace are still said to be bracing themselves for an enquiry from Liverpool, and Doucoure is aware of the Reds' interest in his services.
While the Eagles are planning for the 2023-24 season with Doucoure, the report adds that the capital club would not be in a position to turn down bids between £70m and £80m.
Whether Liverpool are prepared to meet Palace's demands is another question entirely, though, and the Reds could also be facing stiff continental competition for his services.
A separate report from the Evening Standard claims that Paris Saint-Germain are also interested in bringing Doucoure back to Ligue 1, despite already capturing Manuel Ugarte and Cher Ndour this summer.
PSG would have no problem forking out the £70m that Palace are after, potentially forcing Liverpool to scope out cheaper successors to Saudi Arabia-bound duo Jordan Henderson and Fabinho.
The former is now on the brink of completing a move to Steven Gerrard's Al Ettifaq, who have apparently now accepted a bid of £12m from the Saudi Pro League team for their captain, who will earn £700,000 a week in the Middle East.
Henderson was named in Liverpool's squad for their Germany training camp, but he was nowhere to be seen in Wednesday's 4-2 win over Karlsruher SC, while Fabinho was left at home as he negotiates a £40m transfer to Al-Ittihad.
Liverpool have already forked out £95m to sign Dominik Szoboszlai and Alexis Mac Allister this term, and the Reds are believed to view Fiorentina's Sofyan Amrabat, Bayern Munich's Ryan Gravenberch and Manchester City's Kalvin Phillips as alternative midfield options.
The Reds continue their pre-season preparations away to Greuther Furth on Monday before jetting off to Singapore to meet Leicester City and Bayern Munich.