The Denmark captain moved to San Siro on loan for the rest of the 2019-20 campaign in January.
Milan have an option to keep 31-year-old Kjaer in Serie A when his temporary deal comes to an end.
The centre-back has made it clear he wants to remain with the Rossoneri, but a decision is not likely to be made in the near future with the season suspended due to the coronavirus crisis.
Mikkel Beck’s, Kjaer’s agent, told Stats Perform: “The club has a buy-out they can use until a certain date.
“At the moment we are obviously in a position of having to wait to know if they will take use of the buy-out clause.
“We hope they will because Simon is very happy at the club and he’s played very well. We have to wait and see but we are hoping for a positive answer from Milan, because he would like to stay.”
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