The Premier League outfit are currently looking for a new manager following the departure of Sam Allardyce earlier this week.
Allardyce’s contract was not renewed, which means that the Hammers will have a new man at the helm next season.
Sullivan has not named the candidates the board are looking at, but he has assured the fans that they will make a decision soon.
“It is a constantly changing landscape but we are being absolutely thorough in our search, by speaking to representatives of a number of managers and doing our own due diligence on each one,” the 66-year-old wrote on West Ham’s official website.
“Given that, I am not expecting us to make an appointment for at least a week as we must do everything we can to get this appointment right.
“What is clear from our discussions so far is that this job is attracting names it wouldn't have done five years ago.
"When you combine our move to one of the best stadiums in Europe in 16 months' time with the Board's ambitious vision and significant transfer budget you have an extremely exciting prospect for the right man.”
It makes sense for West Ham to take their time and appoint the best manager available. After all, the club have lofty ambitions for the future.
The Hammers are looking to make themselves regulars in Europe in the coming years, and they do need someone with a European pedigree.
Although Allardyce did a truly remarkable job at the Boleyn Ground, the Englishman is not someone who could have taken the club to the next level.