According to Portuguese outlet O Jogo (via Sport Witness), United manager Jose Mourinho is "attentive" to the 22-year-old, who has been heavily linked to the Manchester outfit lately.
It is little surprise United have been linked with a left-back given it is a troublesome position for the Red Devils at the moment.
Luke Shaw continues to find minutes hard to come by and reportedly fears his United career is "effectively over" given his poor relationship with Mourinho, per Jamie Jackson in the Guardian.
Daley Blind, Matteo Darmian and Ashley Young have all operated in the left-back role for United this season, but there is no obvious first choice in the position.
It would be a big surprise were a new left-back not added to Mourinho's squad at some point in the next two transfer windows, and Grimaldo is an exciting potential target.
A graduate of the Barcelona academy, the Spaniard moved to Benfica midway through the 2015-16 season and signed a deal to 2021.
Grimaldo boasts a number of the attributes vital for a modern full-back. He is defensively solid but also a threat going forward, while he has impressive delivery and is a threat from set pieces.
A previous report in Record (via Lucas Sposito of Sport Witness) revealed Grimaldo is "protected by a €60 million (£53.3 million) release clause."
That would be a lot of money for United to splurge on the young left-back, but he could be worth it if he made good on his potential and solved the Manchester outfit's current issues in the role.