The Italian league leaders want the 23-year-old to take part in training on Friday so that he can be included in their squad to play Atalanta on Saturday.
Paperwork is being exchanged between the clubs and the England international is due in Milan for his medical today.
Fikayo Tomori is expected to wrap up the final details of his loan move to AC Milan tonight
Tomori will join on a season loan with the option to make the transfer permanent for £26m.
Chelsea left-back Baba Rahman is also weighing up his next loan move away from Stamford Bridge.
The Ghanaian, who joined from Schalke for £14m in 2015, made 23 appearances for Chelsea in his first season but has been blighted by injuries since and has had spells on loan at Schalke, Reims and Mallorca.
The 23-year-old has made four appearances in all competitions for Chelsea this season
Left back Baba Rahman is also weighing up his next loan move away from Stamford Bridge
He has offers from three clubs that he is considering, including options in England, and hopes to make a decision over the weekend.
Chelsea remain in a state of flux with manager Frank Lampard fighting to cling onto his job.
The 42-year-old is under extreme pressure to turn around results and performances after £200m being spent on players in the summer.
Kai Havertz and Timo Werner have struggled to settle and German coaches Thomas Tuchel and Ralf Rangnick are being considered as potential replacements.