According to David McDonnell of the Daily Mirror, United boss Jose Mourinho wants at least one new centre-back at Old Trafford, having struggled to settle on a regular partnership this term.
McDonnell noted United are also interested in signing Tottenham Hotspur star Toby Alderweireld, although they view the 29-year-old Greece international as a more realistic target than the Spurs defender.
"Chelsea have also been looking at Sokratis, but United are understood to be at the head of the queue, with Mourinho said to have received glowing reports," McDonnell said.
Although United's defensive record in the Premier League this season is only bettered by that of Manchester City, much of that is attributed to the outstanding talent of goalkeeper David De Gea. The protection in front of the Spain international has occasionally been flimsy.
As Simon Peach of the Associated Press, Mourinho tore into his team for their defending in the recent 3-2 win over Crystal Palace:
Some of the biggest problems for Mourinho this season have been Eric Bailey and Marcos Rojo's injury woes, with the pair starting a cumulative 14 top-flight matches.
Chris Smalling and Phil Jones have been the Portuguese's go-to duo, and while there have been times when they have excelled as a partnership, high-class opponents have occasionally exposed them. Additionally, big-money summer signing Victor Lindelof is still acclimatising to English football.
Links to Sokratis make sense with that in mind, especially if he would be available for a transfer fee in the region of £20 million, the figure McDonnell reported.
He's been a key man at Westfalenstadion since joining Dortmund in 2013. As German football writer Archie Rhind-Tutt relayed, the defender has an affinity with the team:
He's been a big influence on the field, and following players like Mats Hummels and Neven Subotic's departures in recent years, Sokratis is the linchpin of this Dortmund defence.
He is a commanding presence, dominates aerial battles and thunderous in the tackle. Additionally, the Greece international does not panic with the ball at his feet, as WhoScored.com highlighted:
He ticks a lot of boxes for Mourinho, who is renowned for bringing in players in the peak years of their careers and giving them a platform to have an instant impact.
If the chance of a new challenge arises, the 29-year-old would surely be tempted by it. Especially if that offer comes from United, giving him the opportunity to become a defensive talisman at Old Trafford.