The recommendation from London Stadium comes after a joint investigation by BBC Panorama and The Times revealed that seven women have accused Sullivan of sexually exploitative and predatory behaviour. He has categorically denied the allegations.
He stood down as joint chairman of the club shortly before the investigation was broadcast, saying he wanted to focus on fighting what he called "factually incorrect and entirely false, decades-old allegations concerning my personal life". He remains the club's largest shareholder.
The investigation also revealed that Sullivan has been banned from contact with West Ham's women's and youth teams for three years due to safeguarding concerns. London Stadium were unaware of the restrictions until the BBC's report.
Sullivan was banned after a historic allegation about his conduct was raised with the Football Association in 2023. He has previously said the allegation was false and that because he had never met any academy or women's team players "1-2-1" during his 16 years at the club, he accepted what he saw as a "meaningless restriction…for a quiet life".
West Ham were relegated from the Premier League in May and are due to play their first home game of the new season, a Carabao Cup match against Portsmouth, on Saturday.
Sullivan was a regular attendee at the London Stadium last season, where he was photographed watching games from the directors' box.
A spokesperson for London Stadium, the operator of the publicly owned venue, said that "following media reports at the end of the season regarding a safeguarding matter being managed by the club, London Stadium sought further information to ensure it could fulfil its own safeguarding responsibilities".
It said that West Ham had told it that the "matter was investigated and that the club does not consider there to be an ongoing safeguarding risk associated with Mr Sullivan attending the stadium".
However it said that, despite this, it had recommended the businessman stay away from games because of the "potential for demonstrations and anti-social behaviour by some spectators".
Sullivan has previously faced criticism from fans over his running of the club, with thousands joining a protest in September last year calling for his departure.
West Ham declined to comment. It is understood that the club intends to work with the stadium operators to facilitate Sullivan's attendance at games.
Sullivan has not responded to a request for comment.
Meanwhile, presenter Tony Livesey left BBC Radio 5 Live on Monday after 16 years at the station, the corporation announced.
Livesey stepped back from his weekday late night talk show in June, following allegations made against Sullivan. He had previously worked as editor-in-chief of Sullivan's Daily and Sunday Sport publications.
One alleged victim said that Livesey had arranged a meeting between her and Sullivan in 1999.
Livesey said he had "no recollection" of introducing the young woman to Sullivan and that it was "not part" of his job to do so.
He added that he had "great sympathy for a woman who may have become a victim", but rejected any suggestion that he had played "any role whatsoever in that scenario" and said he found the allegation "abhorrent".
