The 29-year-old's existing deal in Paris is due to expire in the summer of 2022, and there has been a host of speculation surrounding the Brazilian's future over the last year or so.
Talk of a return to Barcelona has quietened since the coronavirus outbreak, though, with the Catalan giants struggling financially.
Neymar is widely expected to pen a new and improved contract with PSG, and the club's sporting director has hinted that significant progress has been made.
"We have also been talking with Neymar. We will reach an outcome imminently," Leonardo told Le Parisien.
The attacker has scored 13 times and registered six assists in 18 appearances for the French champions during the 2020-21 campaign but is currently on the sidelines with an adductor problem.