It comes with the Blues having splashed a whopping £600million on new players across the two most recent transfer windows.
Neymar is in shock talks to sign for ChelseaCredit: Getty
According to respected French publication Le Parisien, Chelsea owner Todd Boehly has flown to Paris to enter negotiations with PSG over a deal.
The French side spent almost £200million to bring him to Paris from Barcelona in 2017 and have the Brazilian under contract until 2025.
Despite now being 31, Neymar would continue to command a sizeable fee.
The report comes days after Neymar confirmed he had been in a row with club chief Luis Campos and team-mate Marquinhos.
Neymar has made a final decision over his PSG future according to reports
The fall-out followed PSG’s 3-1 defeat to Monaco last weekend, with Campos accusing some players of lacking aggression.
However, Neymar and Marquinhos were not willing to take the accusation lying down and subsequently hit back – with the altercation getting heated.
The Brazilian was in action last night but was unable to conjure any magic as PSG fell to a 1-0 defeat to Bayern Munich in the Champions League.
The forward has excelled in a more central role under Christophe Galtier this season.
How Neymar has performed this season
He has formed one part of a deadly attacking trident alongside Lionel Messi and Kylian Mbappe.
His return has seen him score 17 goals and add 16 assists in 28 games in all competitions this season.
This is despite a well-documented spat behind-the-scenes with Mbappe.
The superstar also came under heat from his neighbours recently after wildly celebrating his 31st birthday.
Just last month Chelsea splashed a British transfer record fee of £107m on Enzo Fernandez.