However, Herman Hummels, who is also Mats's agent, insists that the Red Devils have not made an approach for the 25-year-old.
"I know Louis van Gaal from his time at Bayern Munich," he told talkSPORT. "He's not contacted me about Mats moving to Manchester though.
"I have heard some rumours, but Mats is happy at Dortmund at the moment and only thinking about the World Cup."
Hummels has spent the past five years with Dortmund after making the switch from Bayern Munich.