The 18-year-old winger recently made his debut for Belgium and also scored his first international goal, leading to speculatin over his departure from Anderlecht.
Liverpool tried to sign him when he was only 15 and have continued to keep track of his development with a view to taking him to Anfield.
Anderlecht have also not ruled out selling the winger if they receive a big-money offer, but the club are desperate to keep hold of him this season.
And according to Belgian daily Het Laatste Nieuws, the Belgian giants have been in talks with Doku’s representatives over offering him a new contract.
The teenager still has two years left on his current deal but Anderlecht are acutely aware of the interest from Liverpool and other heavyweight clubs.
Anderlecht want to offer the winger an improved contract in line with his development and tie him down to a longer deal.
Doku will enter the final year of his contract at the end of next season and Anderlecht want to avoid that situation.