The Frenchman spent last season on loan at Napoli, but had a tough campaign, returning to Stamford Bridge this summer.
Bakayoko was shipped off on loan spells in each of the last three seasons and he is not part of Blues boss Thomas Tuchel’s plans at the club.
The midfielder is linked with leaving Chelsea again this summer as they are keen to find him a new home.
And according to Italian daily Il Mattino, the Blues have offered to loan Bakayoko again to Napoli.
Chelsea want to shed the 26-year-old’s salary from their wage bill and are prepared to let him join Napoli on loan again, free of charge.
Gli Azzurri are on the hunt for a new midfielder but they are not in a position to make huge investments in the transfer market and are yet to bolster that area.
It remains to be seen whether Napoli snap up Bakayoko on loan again, given he had an underwhelming run with them last term.