The Argentina international is keen to move to Anfield but United boss Sir Alex Ferguson has refused to sanction the transfer to his club's bitter rivals.
Heinze and Liverpool's lawyers are currently looking into a letter United gave to the player's agent stating the defender could leave for a certain fee and the dispute is set to go to a Premier League hearing on 20 August.
"I want a quick solution. My lawyers have told me a meeting with the Premier League is possible to advance the matter next week," Heinze told The People.
"The club had guaranteed my transfer if a good offer came in and nobody specified anything about the club whether it be a foreign team or Liverpool.
"I am a total professional and I have always behaved as such. Now I just ask that they respect me and accept what I was promised.
"It is incomprehensible and, that aside, they are affecting me as a professional not being able to go to another club.
"I have respected Ferguson since I arrived at Manchester. I don't want any conflict with United and neither do I have anything against the fans. They have always treated me perfectly and I have given everything for the club."