Heinze is hoping to be given the green light to join the Reds when a Premier League arbitration panel meets to discuss his case on Monday.
Heinze has told Sir Alex Ferguson he wants to leave and favours a move to Anfield, but the Scot will not sanction the 29-year-old's move there.
French champions Lyon have expressed an interest in the Argentine, while Barcelona and Real Madrid are also rumoured to have made an enquiry.
But the former Paris Saint Germain defender wants to link up with Liverpool, and hopes the Premier League's panel grant him his wish.
He told the Daily Mirror: "I am a professional and I am concentrating every day on my career with Manchester United, but now my head is thinking about Monday's meeting and I want a definitive solution.
"My lawyers are optimistic about this case.
"My idea has not changed and my objective is to go to Liverpool. I will always be grateful to United, but now I hope they allow me to get my wish."