Bakayoko has spent each of the last two seasons out on loan, representing AC Milan during the 2018-19 campaign before returning to Monaco, making 23 appearances in his second spell with the Ligue 1 club.
The 25-year-old has since returned to Chelsea but is not part of Frank Lampard's plans at Stamford Bridge and is expected to move on before the October 5 transfer deadline.
According to Telefoot, PSG are keen to sign a new midfielder this summer and have identified the Frenchman as the ideal signing in the current market.
Chelsea are allegedly open to Bakayoko leaving on loan for the 2020-21 campaign but would insist that a future purchase option of €40m (£36.9m) is included in the agreement.
The former Rennes youngster has scored three times and contributed three assists in 43 appearances for his current club.