"The contract we have is 100 percent watertight. We have until April to make it permanent but we'll probably do it before the due date," said Sullivan, who is also a film producer and was speaking at an event to publicise his latest project.
"He is a fantastic player and a fantastic man. By February or March, he will be a permanent West Ham player.
"He could be a top, top, top player. He's already sensational and he could be as good as any player in the world."
Sullivan also heaped praise on injured midfielder Dimitri Payet, who has gained many admirers for some eye-catching performances for the Hammers, having been directly involved in nine goals in his 12 league appearances.
"Payet is the signing of the season. He's the best player I've signed in 25 years. He's a 30 million pound ($44.76 million) player," Sullivan said of a player signed for an undisclosed eight-figure fee from French side Marseille.
"He's a supreme footballer. He makes every player in our side play better. On his day, he's world class, he's unstoppable."
The 66-year-old revealed he approached several high-profile managers as a replacement for Sam Allardyce but was content with the appointment of Slaven Bilic during the close-season.
"We were two hours from getting (Rafael) Benitez and then Real came in. We had agreed a contract and everything," Sullivan said.
"He is a top manager whatever anybody says and I think he'd have done a wonderful job for us.
"We tried (Juergen) Klopp as well but he wouldn't come because he said he wanted a break. But I'm glad with the manager we have got."
West Ham, who are 10th in the league, will look to return to winning ways after four successive draws in Monday's league clash with 12th-placed Southampton.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
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