Hummels considering options at Dortmund
The Germany international has long been mooted as a potential arrival at Old Trafford, having endured a difficult season with Dortmund.
Jurgen Klopp's side have spent much of the last few months in the lower reaches of the Bundesliga and appear unlikely to qualify for next term's UEFA Champions League.
Hummels revealed on Sunday that he would consider leaving Germany, but maintained no decision had been made on his future.
"I am openly saying that I think about my future and am considering what I can imagine for it right now," he told Kicker.
"I'm not a fan of those who ostensibly speak of staying but have secretly completed the discussion.
"Everyone knows how much I like it in Dortmund, but I also want us to have a strong team and a powerful approach.
"I often think that I would definitely like to move abroad one day. Then there are also days when I say that I do not need that.
"Basically, I believe that a foreign country will be good both for football as well as personal development."