A source with close knowledge of the dispute described the situation as unprecedented.
Mr Ivey, a 35-year-old Californian, was playing Punto Banco, when he struck a remarkable winning streak.
The 184-year-old casino initially agreed to transfer the winnings to his bank account, but six weeks on it has returned only his £1 million stake.
Instead it began an exhaustive inquiry.
Staff, including the female dealers at the punto banca table, were interviewed at length amid fears there may have been some form of collusion.
This is thought to have been ruled out now since the enquiry.
While it is unclear what, if anything, Mr Ivey has been accused of, lawyers for both sides are said to be engaged in an increasingly tense stand-off. It is not thought that police have been alerted.
Sources said Mr Ivey played for two nights over the August bank holiday for about seven hours in all.
Suspicions over the win intensified when it was discovered that his companion’s membership of another Mayfair casino had previously been suspended.
The reason for this has not been revealed.
Crockfords, the oldest private gaming club in the world, is owned by Genting, company investigators flew to London from Kuala Lumpur to speak to everyone who was working on the two nights in question and to examine hours of film from surveillance cameras.
The cards used and the shoe they were dealt from were also scrutinised.
‘No imperfections, or marks, that would have given Ivey an advantage were found.
In any case, Ivey at no time touched the cards,’ said a source.
‘The shoe was also thoroughly inspected; once again the investigators drew a blank.’
Mr Ivey, who once picked up £10 million in a poker tournament in Las Vegas, was playing in a small private room on the ground floor of Crockfords.
He sat next to his companion.
The only other people in the room were the croupiers and an inspector.
All the action was recorded on ten cameras.
At the time of publication no comment was made from Crockfords about the incident.