The Premier League new boys have recruited heavily over the course of the summer and raided Serie A over the weekend to complete the signing of midfielder Remo Freuler from Atalanta.
They still have business in Italy and, according to Italian outlet MilanNews.it, are in talks to sign Bakayoko from AC Milan.
Bakayoko is currently in the second year of a two-year loan at AC Milan from Chelsea, with the Rossoneri having an option to buy.
It is claimed that Bakayoko is looking upon a potential move to the City Ground positively and further developments are expected this week.
He would be willing to link up with Steve Cooper’s side if an agreement can be found for him to join Nottingham Forest.
The midfielder has no future at Chelsea and has been shipped out by the Blues on a series on loans.
He played for AC Milan in the 2018/19 campaign, then spending the 2019/20 season at Monaco. A return to Napoli came in the 2020/21 edition of Serie A, while he joined AC Milan again last summer.