Rojo joined Estudiantes on loan in January but only made one appearance before the coronavirus pandemic struck.
His contract at Old Trafford runs until 2021, although United hold an option to extend the deal for a further 12 months. Sources have told ESPN that Boca are keen to sign the 30-year-old permanently if they can agree on a fee.
Manager Ole Gunnar Solskjaer is open to adding another central defender to his squad ahead of next season to challenge first-choice Victor Lindelof but already has seven in the side.
As well as Maguire, Lindelof and Rojo, United have Eric Bailly, Axel Tuanzebe, Phil Jones and Timothy Fosu-Mensah. Highly rated Teden Mengi, 18, has also been training with the senior group ahead of the Premier League's restart.
Rojo is keen to play enough first-team football to force his way into the Argentina squad for the Copa America, now due to be held in 2021 because of the coronavirus pandemic.
The competition was originally set to be held this summer before the coronavirus outbreak, and Rojo was motivated to join Estudiantes in January by the promise of regular games.
He has been capped 61 times by Argentina and played in the World Cup in 2014 and 2018. Rojo joined United from Sporting Lisbon for £16m in 2014 and made 122 appearances for the club, scoring twice.
Solskjaer's players have already taken part in an inter-squad friendly at Old Trafford and were due to face Stoke City at their Carrington training base on Tuesday before the game was cancelled at short notice.