Rojo joined United from Sporting CP in 2014 but has rarely been considered first choice, with injuries a regular problem for him, while he has also seemingly failed to convince incumbent manager Ole Gunnar Solskjaer.
This season the 29-year-old has featured just three times in the Premier League and media reports suggest United are actively trying to offload the centre-back, who is said to be on a wage of around £130,000-a-week.
Argentina international Rojo came through Estudiantes' academy and represented the first team before leaving for a brief spell with Spartak Moscow prior to joining Sporting.
But his family are reportedly eager to return to Argentina, and Veron – a former United player – is hopeful of being able to strike a deal.
He is quoted as saying by La Nacion: "Hopefully United can see that there is no economic issue that we can match, but that it [the deal] happens in other ways and that we can attract him. We are working so that he can come back.
"He has everything to keep playing Europe, but he wants continuity."