The Germany international defender is among the most sought-after talents in European football.
Still only 24 years of age, it is widely acknowledged that a player who has already landed two Bundesliga titles and a European U21 Championship crown will see his progress continue apace.
A fee of around £30million would be required to secure his services, but the top clubs on the continent would have no problem generating such funds.
Barcelona are said to be leading the transfer chase, with the Catalan giants in the market for a long-term replacement to talismanic skipper Carles Puyol.
Hummels is reported to be their preferred choice, but Dortmund insist no sale has been sanctioned as yet for a player who remains under contract at Signal Iduna Park until 2017.
General manager Michael Zorc told Ruhr Nachrichten: "About 99.9 per cent of all professionals would want to listen to an enquiry from a club the size of Barcelona.
"But it's pure nonsense that we have granted permission (for a summer transfer)."