Blaise Matuidi and Juventus are prepared to extend his current contract to June 2021, according to Tuttosport.
The 32-year-old had been expected to leave last summer when new coach Maurizio Sarri took charge, but has won over the tactician with his performances.
His contract is due to expire in June 2020, but Tuttosport claims there is a clause that can be exercised unilaterally to extend for one more year.
The France international has 14 competitive appearances for Juve this season, scoring one goal.
Matuidi has been with the Bianconeri since making the €25m move from Paris Saint-Germain in August 2017.