The Argentine and his manager held face-to-face talks for the first time this summer on Monday in a bid to resolve the row over Heinze's proposed move to Liverpool.
Heinze had pledged to report for duty as ordered by Ferguson and duly arrived at United's Carrington training complex following a brief break after his Copa America campaign.
Ferguson has insisted he will not allow the 29-year-old to move to Anfield and while the content of their discussions on Monday was not immediately revealed, Heinze has now admitted he wants out.
He told the Daily Mail: "I've spoken to the coach and I have insisted that my wish is to leave the club if a big offer appears on the table.
"Today, the only such offer is from Liverpool and it is this that is causing the problem.
"Earlier in the summer I received a promise from United that I could leave if the deal was good for both parties and at the moment there is an offer from Liverpool."
Heinze admitted he "understood" Ferguson's position but is now seeking legal advice.
He added: "The coach is serious about this and I understand his view. But I am serious too. My lawyers are studying the situation and I'm going to wait for a few days to get a full report from them."
The Daily Telegraph, meanwhile, claims the saga could be resolved as soon as next week.
It reports that a three-man Premier League arbitration panel will meet early next week at Heinze's request in an attempt to find a solution.