Manager Stefano Pioli has said he would like to see a new central defender come through the door at San Siro this month, given their mounting injury crisis.
Until Matteo Gabbia was recalled from his loan at Villarreal, Theo Hernandez was forced to play in the centre, due to injuries to Fikayo Tomori, Malick Thiaw and Pierre Kalulu.
The shortage of defensive options at Pioli's disposal saw Corriere dello Sport claim that the Rossoneri were exploring the opportunity to sign either Kiwior or Chalobah this month.
Neither player is a regular at their respective clubs, as Chalobah has not played a single minute in any competition at Chelsea this season.
Kiwior is also down in the pecking order at Arsenal, with most of his football coming in cup competitions so far.
The 23-year-old started in Arsenal's 2-0 FA Cup third round defeat to Liverpool before the winter break, scoring the own goal which put Jurgen Klopp's side ahead late on.
After being put off by Brest's €10-12m price tag on Lilian Brassier, Milan are seeking alternatives that they can sign on loan this month.
However, the report states that Arsenal are uninterested in entering negotiations in a deal which would see Kiwior move to San Siro on loan with an option-to-buy in the summer.
In addition to this, Kiwior's agent has also come out to say that a move away from the Emirates is unlikely in January.
Speaking to Polish outlet Kanal Sportowy, agent Pawel Zimonczyk said: "Kuba is an Arsenal player, there are no signs that they want to get rid of him and I don't think anything will happen in the winter window."
With Chalobah not in the plans of Mauricio Pochettino at Stamford Bridge, a loan move could be more plausible, but Milan are said to be reluctant to contribute towards the defender's wages should he move this month.
As neither player is currently starting at their clubs though, Milan remain confident that any potential deals could become more likely as the window draws to a close.
Kiwior and Chalobah are not the only names on Milan's shortlist though, as reports on Monday linked Everton's Ben Godfrey with a move to the Serie A club too.