The Red Devils are in hot pursuit of Varane as he seeks an exit from Spanish giants Real Madrid.
Varane, who has been linked to United in the past, is out of contract at Real next summer.
According to El Confidencial, Real wanted to keep the 28-year-old, but now prefer to cash in on him this summer.
They deem a fee of £43 million as a success, if United agree to pay such a sum.
Varane will double his salary if he joins the Red Devils, who have agreed to his demands.