The 23-year-old German international has been in scintillating form in the Bundesliga this season, and his form has not gone unnoticed by a number of Europe's biggest clubs.
Red Devils boss Sir Alex Ferguson is keen to bolster his defensive ranks at Old Trafford this month, with club captain Nemanja Vidic ruled out for the remainder of the season, and a number of other injuries having depleted the Manchester United squad.
However, the reigning Barclays Premier League champions will face competition for Hummels' signature from local rivals City, as Roberto Mancini also looks to add more competition to his backline.
But, any hopes either club may have had of signing Hummels in January have been dashed after the player told German newspaper Bild that he wants to remain in Dortmund.
"I am happy playing for Borussia Dortmund and I want time to challenge for more trophies," he said.
The German press expects Hummels to make a decision over his long-term future at the end of the 2011-12 campaign, giving hope to both Manchester United and neighbours City, that he would consider a move to England in the summer.