The Argentine defender returned to his boyhood club in the January transfer window after agreeing a loan move until the end of the season.
However, Rojo made just one appearance following an injury lay-off and has now seen the football season suspended amid the ongoing coronavirus pandemic.
"His desire is to stay," Desabato told La Nacion.
"The little I talked to him at this time about the stop is that he'd like to continue playing until January of next year. But there are things that don't depend on him. It doesn't end with him deciding.
"In this squad that I have there are many kids, his presence can do them very well."
Rojo's loan is due to expire on June 30.
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