The wantaway Paris Saint-Germain full back is reportedly wanted by both Jose Mourinho and Luciano Spalletti.
Aurier has a year left on his contract with PSG and has refused sign a new long term deal in a bid to force through a move.
He was left behind by the Parians in their recent preseason tour.
Unai Emery has since moved and captured his replacement by signing Brazilian full back Dani Alves and now the Paris side awaits offers for the Ivorian international.
According to psgunited, Mino Raiola -who played a key role in United’s snatching of Romelu Lukaku from under the noses of Chelsea- has approached Arier's agent, Stephane Corbis over a possible transfer of the 25-year-old to Old Trafford.
But the Premier League giants are not alone in the race to sign the 24-year-old with SkySports also reporting that Inter Milan are willing to cede Joao Mario and a small check of 30 million euros.
Tottenham Hotspur and Juventus are also reported to be keeping tabs on the player as they are on the lookout for replacements of Kyle Walker and Alves respectively, while Barcelona have also been linked with the Elephants' captain.