The Barcelona right-back played in a starring role in his side's 3-1 Champions League final win against Juventus on Saturday night.
Alves is out of contract in the summer and United are leading the chase for him as they seek a replacement for Rafael.
So far, the Brazilian has refused to commit his future to the Catalan giants.
It would be a pleasure to join Milan
Dani Alves
And the 32-year-old admitted in the aftermath of Barca's Champions League triumph why Milan would be a tempting proposition.
"It would be a pleasure to join Milan," he told Sky Sport Italia.
GETTY
Dani Alves wouldn't mind joining AC Milan
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"It is a possibility and I am considering all the offers."
Alves' wage demands of £4.3million a season could prove a stumbling block to any potential move.