United disputed claims from Heinze, 29, who said the Red Devils gave him written permission to pursue a transfer to another club for a fee of £6.8m.
But a Premier League arbitration panel concluded that the permission "was unambiguous in that it envisages only an international transfer".
The defender is set to appeal against the panel's decision.
However, with the transfer window scheduled to shut on 31 August, he is short of time if he wants to leave Old Trafford.
The arbitration panel's verdict read: "The Premier League Board-appointed panel have heard submissions of evidence from both parties and has ruled to dismiss the player's case.
"The hearing concluded that nature and intention of the disputed 13 June 2007 letter, especially when taken in context of verbal discussions and Manchester United FC's transfer policy, was unambiguous in that it envisages only an international transfer.
"Furthermore, the hearing finds the letter constitutes an 'agreement to agree' and did not create an obligation or binding agreement for the club to transfer the player to any particular club."
United manager Sir Alex Ferguson and chief executive David Gill travelled to Monday's hearing in London to put their case and will be happy with the verdict.
A Manchester United spokesman said: "We are pleased that the panel has endorsed our case."
Too bad mate, but to me the move never made much sense in the first place but I will be interested to see how this will affect his happiness and his form if Fergie plays him. This ruling has led to the Free Heinze campaign, coming to a t-shirt store near you: