The Red Devils have been tracking the Colombian star, who has also been linked with Chelsea, for some time, and are believed to have made him one of their top summer targets.
Old Trafford chief Sir Alex Ferguson has reportedly contacted Porto recently to enquire as to their willingness to accept Nani as part of any deal.
The Portuguese wide man has struggled for first-team this season, with a public falling out with Fergie doing little to aid his chances of becoming a regular starter.
Although the club have insisted that he is still in their plans, they are said to be willing to allow him to leave.
Porto are believed to be far from keen to lose Rodriguez, but Fergie is hopeful that offering them a direct replacement may alter their stand point.
The 20-year-old South American is widely regarded as one of the finest talents in European football, and has been a key member of Porto’s first-team for some time, despite his youthful age.
AC Milan reportedly made a £20m offer for Rodriguez last summer, but his employers quickly knocked this back.
United are also planning to axe Federico Macheda, Bebe and Patrice Evra this summer.