The 21-year-old picked up an assist in the Champions League this week for the Eagles, though they went on to lose 2-1 against CSKA Moscow.
According to O Jogo, Red Devils boss Jose Mourinho has tasked the club's scouts with keeping a close eye on Zivkovic after being alerted to the youngster's potential last season.
The report goes on to claim that those scouts had been monitoring Benfica matches even before the two clubs were drawn to face each other in the Champions League group stages this season.
Zivkovic has long been regarded as a potential top player in Serbia after making his debut for Partizan Belgrade as a 17-year-old, even going on to become the club's youngest captain.
The attacker recorded three assists for Benfica last season, coming into the side in the second half of the campaign and duly becoming a mainstay in in the first team.