Lanzini has managed to impress many with his performances in the Premier League since joining West Ham from UAE side Al Jazira on loan during the summer.
West Ham are now understandably keen on signing Lanzini on a less temporary deal and have until April 2016 to facilitate such a move, however, Sullivan has gone on to state that the club are looking to seal the deal for Lanzini much sooner.
Sullivan said: "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 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."