However, Massimiliano Mirabelli, the club's sporting director, insists Milan have no inclination to allow the 19-year-old to leave the club, despite their exit from the Europa League.
"Apart from his mistake, he played a great game tonight," Mirabelli told reporters.
"We want him to stay with us for a long time. He's a gem of ours and the whole of Italy, and we're keeping a tight grip on him."
Reina is expected to join Milan in the summer and reports claim that the former Liverpool goalkeeper has already undergone a medical.
Donnarumma has been capped four times by Italy, and has made a total of 113 competitive appearances for Milan.
Italy will have four places in the Champions League next season, with Milan currently in sixth position, five points behind fourth-placed Lazio.
Milan do have a game in hand on Lazio and face Chievo at home on Sunday in their next game in the quest to qualify for the Champions League.