The Blues are open to letting their 29-year-old winger leave the club in January after signing multiple attackers, including Mykhailo Mudryk, Noni Madueke and Joao Felix.
It remains unclear whether an option to buy will be included as talks continue but all parties are positive that a deal to see Ziyech remain in Paris for at least six months will be concluded.
The World Cup semi-finalist has been keen to leave Chelsea for almost a year after losing his place under Thomas Tuchel and he has only recently regained it due to an injury crisis in west London.
Chelsea have fielded interest from Newcastle but declined to allow the Morocco international to strengthen a Premier League rival.
Meanwhile, Everton, Roma and AC Milan have all been tracking Ziyech in January after Manchester United expressed an interest in signing him over the summer.
Ziyech’s current Chelsea contract expires in 2025, raising the prospect of a possible return in the summer.