The 22-year-old has been very impressive during his time at the Boleyn Ground.
The 22-year-old is currently on loan from Al-Jazira, but Sky Sports reports that the Premier League side have the option to make the deal a permanent one any time before April. And Sullivan explained that the club plan to exercise that clause in the coming months, ahead of schedule.
"The contract we have is 100% watertight. We have until April to make it permanent but we'll probably do it before the due date," he said.
"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."
It is no surprise that West Ham plan to make the move permanent as the playmaker has been excellent for Slaven Bilic's side this season. His four goals have helped the club maintain a position in the top half, well placed for a potential charge at a possible European spot for next season.
His presence has been hugely missed, however, by his side since he sustained an injury against West Brom last month. Without him, West Ham have failed to win a single game, drawing all four fixtures, and scoring just once.
With the side struggling for form, he will be desperate to prove why the Hammers are so keen to make his deal permanent upon his return.