The centre-back has been told he can leave this month to get more regular game-time – but Frank Lampard is adamant he wants any move to be temporary.
Yet negotiations with Milan have led to discussions of a potential option to buy if he impresses in the second half of the season.
Tomori has been restricted to just one substitute appearance in the Premier League this season.
The arrival of Thiago Silva in the summer has pushed him down the pecking order, with Kurt Zouma, Antonio Rudiger and Andreas Christensen also ahead of him.
Milan are keen to bring Tomori in to boost their Serie A challenge in the second half of the campaign and have been encouraged by Chelsea’s willingness to let him go.
But Lampard claimed last week that he sees his future at Stamford Bridge.
He said: “He absolutely has a long-term future at this club and we will see if and when he goes out on loan.
“The moment I got close with Fikayo is when I took him on loan to Derby and he was the player of the year and one of the best players in the Championship that year.
“He came back last year, played 20 plus games for us at a young age and then got in the England squad.
“There is a long-term plan for Fikayo in my head about his career here. And if he goes out on loan it will be to enhance his personal development, hopefully, help the team he goes to, and come back as a better player.”