Reports last month stated the United right-back was wanted by both Inter Milan and Juventus.
But sources have told sportinastorm.com that the Red Devils still remain in the dark.
United are believed to be happy to facilitate a loan move until the end of the campaign, with an obligation to purchase.
They are also looking to recoup the majority of the £12.7m figure they paid to Torino for his services last year.
The Italy international defender is still respected in his homeland but United fear Serie A clubs are currently making them sweat.
Darmian has made just seven appearances this term although he had already fallen out of favour under former boss Louis van Gaal.
Ironically, the 26-year-old has started United's last two games, against Arsenal and West Ham, with Jose Mourinho playing him at left-back due to injuries and concerns over Luke Shaw's form.