PSG are open to offloading the 30-year-old this summer following a difficult campaign in which the French club’s fans booed the Brazilian at the Parc des Princes following their Champions League exit in March.
However, Neymar’s departure is a difficult prospect due to his annual salary of €43 million (£36.4m) before bonuses.
Chelsea are among the small number of clubs who could potentially afford to sign Neymar and the club’s new co-owner, Todd Boehly, has held talks about the possibility of bringing the Brazil international to Stamford Bridge.
However, the Evening Standard reports that Tuchel is ‘lukewarm’ to the idea of having Neymar in his squad.
The report claims that Tuchel is also not keen on the prospect of Chelsea signing Cristiano Ronaldo as he wants his attack to be more fluid.
However, it’s also said that Tuchel’s stance on Neymar, who he’s already managed at PSG, could change later in the window if Chelsea struggle to bolster their attack.
Tuchel is on the verge of welcoming Raheem Sterling into his squad after Chelsea agreed a £47.5 million fee with Manchester City.
Sterling has already completed part of his medical and could link up with his new Chelsea teammates who are in the United States for their pre-season tour later this week.
Elsewhere, Chelsea are set to miss out on signing Raphinha, despite agreeing a £55m deal with Leeds United weeks ago.
It’s understood that Barcelona have submitted a £63m offer and Raphinha has been holding out for a move to Camp Nou.
For more stories like this, check our sport page.