The 24-year-old is widely regarded as one of the brightest young defenders in the Bundesliga, and has attracted admiring glances from a host of top European clubs.
Red Devils boss Sir Alex Ferguson has been credited with an interest in bringing the Germany international to Old Trafford, as he looks to strengthen his centre-back options ahead of the 2013/14 campaign.
With Nemanja Vidic struggling to shake off continuous injury problems and Rio Ferdinand yet to extend his contract that expires at the end of the season, there could be an opening this summer.
However, Manchester United now face serious competition to secure the Dortmund defender's signature, after Hummels admitted that there are only two or three clubs he would even think about signing for, one of which is Barcelona.
"My father and I would turn down about 99.9 per cent of all the clubs in the world if they approached us," he told Sport Bild.
"However, Barcelona are one out of two or three teams that could make me consider a summer transfer."