Milinkovic-Savic spent last season on-loan with FK Vojdinova and United want to send him away again to continue his football education.
BILD says the 18 year-old Serb kicked off his trials with Darmstadt yesterday.
Milinkovic-Savic has been offered the chance by Darmstadt to compete for the No1 spot, should he do enough to be taken on-loan this week.
The goalkeeper is tied to United until 2019.
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