Senior Old Trafford sources have hinted they have heard nothing back after contacting the 27-year-old central defender's representatives in the last few weeks, with a view to offering improved terms.
Rojo has 15 months left on his contract and Jose Mourinho has already made it clear to the Argentina international that he wants him to remain an integral member of his squad.
United are understood to have failed to include an option to extend Rojo's contract by a further 12 months when they originally signed the player from Sporting Lisbon back in 2014 for £16m, which is another reason why they are keen to nail down a firm commitment.
The South American has had his fair share of injuries in the last 18 months but he has been able to win over Mourinho with his attitude and ability to also play at left-back.
Rojo earns around £100,000-per-week at United, who are fearful of rumblings that Paris Saint-Germain could be hovering in the background.