The 23-year-old's future at the Parc des Princes has come under increasing speculation having entered the final year of his deal, and he is free to discuss terms with clubs in January should an extension not be agreed beforehand.
The Metro reports that Rabiot is eager to rejoin City, where he spent a year at the academy before leaving due to homesickness at the age of 14.
Rabiot is still reportedly appreciative of the efforts and understanding of City during that time, giving them the edge in the race for his signature.
The likes of Barcelona, Juventus and Liverpool have also been linked with a move for the French midfielder, and PSG could still look to cash in on Rabiot by accepting an offer during the January transfer window.
City are hopeful that Rabiot's desire to join the club will convince him to bide his time and leave on a free next summer, though, with Pep Guardiola's side understood to be unwilling to make a move in January.