The Germany international is reportedly valued at £30m by Dortmund, who are desperate to keep hold of him despite interest. Manchester United and Arsenal have been mentioned as potential suitors, with Louis Van Gaal believed to be an admirer of the 25-year-old.
But that asking price may have put off United, who also have their eye on a much cheaper alternative in the shape of Arsenal defender Thomas Vermaelen.
The Belgian international wants first-team football, and Arsene Wenger has admitted this month that he could leave the Emirates Stadium before the September 2nd transfer deadline. He is available for between £10m and £12m.
Van Gaal has identified Vermaelen and Hummels as ideal for his planned 3-5-2 formation he intends to use for the first few months of the season at least. He's experimented with Jonny Evans, Chris Smalling and Phil Jones at the back, but United have no depth at the position beyond those three.
Academy graduate Michael Keane has been used in preseason and remains a highly rated prospect, but Van Gaal is believed to feel that he needs another experienced Champions League campaigner in his back three to make it work.
Dortmund holding firm
Hummels would have been the prize catch, but after the bitter departures of Robert Lewandowski and Mario Gotze in consecutive summers, Dortmund are clinging on to the World Cup winner.
The report claims Hummels wanted a move to Manchester United, but Dortmund's tough negotiating stance has ended any hopes of a move. Arsenal were also thought to be monitoring his availability, with a view to a bid once Vermaelen had moved on - either to United or Barcelona.
The Catalan giants have reportedly lodged a £10m offer for the versatile Arsenal defender.