The Rossoneri are without three senior centre-backs due to injury and are in desperate need of fresh resources.
And according to La Gazzetta dello Sport, the out-of-favour Blues pair are among the options, while Sao Paulo's Rodrigo Caio is also being pursued by sporting director Leonardo.
Christensen enjoyed his breakthrough campaign under Antonio Conte last season, but Maurizio Sarri's arrival in the summer has coincided with his opportunities becoming limited.
The Denmark international has made just six appearances this season, none of which have come in the Premier League.
Cahill, 32, has also been shifted down the pecking order, making just six outings this term, and just once in England's top flight.
A loan move in the New Year appears the most like option, with Milan's senior players preferring a move for 22-year-old Christensen.
Having gone from being a central figure of the Chelsea first team to a peripheral member of Sarri's plans, the Dane is growing increasingly frustrated.
He said: "There's a difference from last season. I played a lot of games but this season hasn't been like that.
"It's always difficult for a player but we'll see what happens."
Asked whether he could hand in a transfer request in an effort to manufacturer a move away from Chelsea, he added: "It’s a difficult question.
"If you asked every player that’s not playing if they’re happy they’ll say 'no'.
"Everyone wants to play but you know I can’t do anything but train and do my best when I get the opportunity.
"I have to perform well to show him [Sarri] that he can count on me. You don’t want to sit around and wait for it you want to play straight away – that’s why we play football.
"Not playing is not fun but it’s a different situation to last season."
As Christensen looks set to leave Stamford Bridge, the manner of his arrival six years ago is riddled in controversy.
He joined the club as a 16-year-old on July 1, 2012 from Brondby.
But according to a report by Football Leaks the west Londoners began employing his father Sten on the same day as a scout.
He was allegedly paid a monthly salary of £11,400 over four years – a total of £656,640 – alongside working at Brondby as a goalkeeping coach.
Payments to family members of prospective youth players are banned, with both Everton and Liverpool having been reprimanded in recent years.
Premier League clubs are pushing for an investigation into the findings which could lead to a transfer ban preventing the side from signing youth players in the future.
A Chelsea statement read: “We do not comment on speculation concerning confidential contracts or player-related matters.”
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