Rojo returned to El Leon in January but only featured on one occasion for the club before the coronavirus outbreak halted the majority of football across the globe.
As it stands, the 30-year-old's loan deal at Estudiantes is due to expire at the end of June, but Desabato has claimed that the Argentina international is determined to stay at the club.
"We want him to continue at the club and he wants to stay. I speak to him very often and he is happy to be here," Desabato told Jogo Bonito.
Rojo has made 122 appearances for the Red Devils since arriving from Sporting Lisbon in 2014, but he has struggled to secure a regular spot this season, featuring on just nine occasions in all competitions.
The South American's current deal at Old Trafford is due to expire next summer. body check tags ::