According to the Daily Mirror, United have been made aware of Dortmund's long-standing policy of refusing to let more than one star player leave every summer, with a double deal for Gundogan and Hummels seemingly unlikely.
The Bundesliga club confirmed last week that Gundogan has refused to extend his stay at Signal Iduna Park beyond 2016. That means he would have to be sold this summer in order to avoid a repeat of Robert Lewandowski's free transfer to Bayern Munich in 2013.
In recent weeks Hummels has publicly admitted that he is considering a future away from the club he first joined, initially on loan in 2008, prompting interest from a number of top European sides.
There is also the future of Marco Reus to consider, even though transfer talk has died down since he signed a new contract. The winger still remains one of the world's hottest commodities and should a suitor come in with a bid it could also affect United's ability to land Hummels in particular.
The one shred of hope for the Old Trafford hierarchy comes with the uncertainty following Jurgen Klopp's decision to walk away from Dortmund.
There is an understanding that the club may be willing to break recent habits and sell a number of players in order to give new boss Thomas Tuchel the funds to shape a new squad as he wishes.
If United are unable to sign Hummels this summer there is every chance the club will look elsewhere for a new centre-back to strengthen their defensive ranks, with Valencia's Nicolas Otamendi another rumoured target.