United scouts were present when the 21-year-old picked up an assist in Benfica's home defeat to CSKA Moscow, following instructions of United boss Jose Mourinho.
As reported by Portuguese outlet 'O Jogo', the former Real Madrid and Chelsea manager is a keen follower of football in his native country, and was alerted by the youngster's potential.
The scouting reports that have been sent back to Mourinho have been positive, following stand-out performances from the Serbian winger at the Estadio da Luz early this season. Zivkovic joined the Portuguese champions in the second half of last season and recorded three assists.
Benfica boss Rui Faria, known for his career long association with Mourinho as his loyal assistant, is fond of Zivkovic, whose contract in Lisbon runs until 2021, with a release clause set at 60 million euros.