Rojo was supposed to return to United when his loan with Estudiantes expires on June 30.
However, United boss Ole Gunnar Solskjaer says he will remain in lockdown in Argentina.
"Marcos has been in lockdown over there [in La Plata], so they've not played either," said Solskjaer.
"At the moment, I can't see him coming back here over the summer, obviously because we live in this bubble, and we've got this squad available until next season.
"So he just needs to focus on getting fit and staying fit and being ready for wherever that takes him."