The Dane is currently on-loan at Milan from Sevilla.
“Milan and Sevilla have reached an agreement to extend the loan with an option to buy until the end of the season," agent Mikkel Beck told Sport Mediaset.
“Kjaer pictures his future at Milan and the coronavirus situation has not changed his mind. He is doing a fantastic job with the Rossoneri, through some excellent performances and achieving good results.
“The team have improved since he arrived in January and the fans welcomed him in an extraordinary way."