Express Sport understands Benitez is open to managing the Hammers if they give him a £100m transfer budget, total control over signings and a £6m-a-year contract.
According to Chilean media outlet Pauta, the 64-year-old has agreed to leave his current club in China in order to take the reins vacated by David Moyes last week.
West Ham announced the departure of Moyes on Wednesday and said a new manager would be hired "within the next 10 days".
The post comes after the Hammers had been linked with Newcastle United manager Rafa Benitez in what would seemingly be, by all accounts, a much more popular appointment than the former Leicester City manager.
As per the Telegraph, "Benitez is also seeking reassurances from the sport shop billionaire that he will be able to spend the money when and how he wants, rather than have to wait for weeks for deals to be signed off, which was a cause of tension 12 months ago".
On who should replace Moyes, Hislop added: "I do [like the idea of Pellegrini], if you can get him".
Their preference is to hire a manager who has worked in the Premier League, although they have not denied making contact with Shakhtar Donetsk's Paulo Fonseca last week.
West Ham have had their own issues with ownership, ones where tempers reached a fever pitch during the 2017-18 season. "Where actually does the club wanna go?"
"If they don't spend, Newcastle, then obviously to get the maximum out of them players again is very hard, that'll be three years running, with the same basic squad", he added.