The Argentinian has been blighted with injuries in the last few years and has seen himself fall well down the pecking order in the centre-back department, starting just one Premier League game last term and playing just nine games overall before returning to his home country on loan.
United were believed to be looking for a buyer for the 30-year-old but with his contract ending in June, time is running short and it may now simply be a case of saving his wages by letting Chris Wilder take him for half a season.
‘Rojo is a free agent at the end of the season and needs a long-term move,’ says The Sun’s Alan Nixon.
‘Half a season with the Blades may appeal.
‘Wilder lost influential defender Jack O’Connell to a knee injury and still has a loan space.
‘And he is hopeful he can agree a deal with United.’
Allowing the move would be a fair thing for the Red Devils to do as it would allow Rojo to gain match fitness and put himself in the shop window ahead of the summer.
However, United are not known to be particularly honourable in these situations and may be more difficult to persuade than Wilder thinks. They could instead opt to spend the month of January scrabbling around trying to find someone who is willing to pay a couple of million pounds for the World Cup finalist, making it much harder for the player to find a club in June if they fail.
This summer’s transfer window has been one of the strangest in living memory. So cast your mind back to less stressful days and test your knowledge of past United arrivals and departures in our quiz below.