The American was challenging a Court of Appeal judgement that the Crockfords Club could refuse to pay up cash Ivey won playing card game punto banco.
The club said Mr Ivey had broken its rules by using an "edge-sorting" technique to spot advantageous cards.
Mr Ivey had consistently argued that he had merely used a legitimate advantage
But, according to Sky Sport Italia, Everton may need to act fast as West Ham are also tracking the former Watford manager.
Crockford's owner, Genting Casinos UK, said the two players jointly used the technique of "edge-sorting", which involves identifying minute differences in the patterns on the back of playing cards and exploiting that information to increase the chances of winning. Genting said this was not a legitimate strategy.
However, Mr Ivey contended that the technique was not a form of cheating because it did not involve dishonesty.
He said that he had merely exploited Crockfords' failure to take proper steps to protect itself against a gambler of his ability - and he was therefore entitled to his full winnings, rather than just having his initial £1m stake returned to him.
The five Supreme Court justices unanimously upheld the Court of Appeal's decision on the case in 2014, with Lord Hughes saying it was essential that punto banco remained a game of pure chance with neither the casino nor the player being able to beat the randomness of the cards that were dealt.
He said: "What Mr Ivey did was to stage a carefully planned and executed sting."