The report notes United scouts were in attendance as Sporting beat Olhanense 1-0 at the weekend courtesy of a Carlos Mane strike.
And while many media outlets have reported United's interest in midfielder William Carvalho, the Daily Mail also claims United were watching left-back Rojo as well.
The 23-year-old is an Argentina international with ambitions to go to the World Cup this summer.
United boss David Moyes is thought to be on the lookout for a left-back, with current first-choice Patrice Evra tipped to depart at the end of the season.
The Frenchman's contract expires at the end of the season, and back-up Alexander Buttner has not put forward a strong case to take his place going forward.
But it appears he is also looking further afield with Rojo under consideration as well.
William Carvalho, who made his first Portugal international appearance last year in the World Cup playoff against Sweden, has also been heavily linked with the defending Premier League champions.