The former Portsmouth boss will replace the recently sacked manager Gianfranco Zola.
“It’s virtually a done deal and it’s almost certainly Avram Grant,” said Sullivan in an recent interview with The Daily Mail.
“We believe in going with experience and Avram has 34 years’ experience.
“I like him very much. He’s completely the opposite of what I imagined. I imagined a dour, boring, serious man with no humour. In fact he’s got a very dry sense of humour with an almost encyclopaedic knowledge of football. Wonderful. He tells jokes and stories. He’s led a full life and he’s learned from that.
“He will get a four-year contract but we won’t judge him for two or three years, by then we’ll see if he’s as good as we think he is. He will inherit a very unbalanced team and it will take time to sort out with the limited resources we have and the inflated transfer fees and wages.
“We interviewed three or four others. One said he would come but wanted £7m in wages for him and his staff. Another said he’d come but would want a minimum transfer budget of £40m. And another was thinking of coming until he had an offer from elsewhere that was too good to refuse.
“Avram is the man for the job. A superb candidate with a very good record. What he did at Chelsea was under-rated. The team were going backwards when he took over and he almost won the Champions League and the Premier League.
“He did very well at Portsmouth. He wasn’t there from the start of the season, he inherited a team which was ripped apart underneath him, he had points deducted, but he got them to the FA Cup final. With his points-per-game they would have stayed up.”