Both clubs have received a boost in their pursuit of the France Under-21 international, whose future in the French capital is looking increasingly uncertain.
The midfielder is set to enter the final year of his contract in the summer, and the French champions have offered him an extension.
However, the player has not agreed to the new contract, and reports in France suggest the two parties are a long way off agreeing a deal.
Rabiot is keen to be given assurances he will have more first team opportunities, although that may prove difficult given the star-studded nature of PSG’s squad.
And that could open the door for both Arsenal and Chelsea in the summer, with both London clubs having expressed an interest in the talented 18-year-old.
Both clubs are keen to add more young talent to their squads in the summer, with Arsene Wenger reportedly especially keen to complete the signing of his fellow countryman.