Sky Italia says Milan management want to add a new centre-half signing to Stefano Pioli's squad this month and Christensen is high on the agenda. Fellow Dane Simon Kjaer, currently with Atalanta on-loan from Sevilla, is also under consideration.
Milan are looking at Christensen as an alternative to Barcelona youngster Jean-Clair Todibo.
Chelsea are open to selling Christensen this month, though Milan would prefer an initial loan arrangement.
The defender has seen Fikayo Tomori move ahead of him on the defensive pecking order this season.