Avram Grant looks set to be unveiled as West Ham's new manager in 12 days' time.
Reacting to speculation that Grant's move to the Hammers was all-but signed and sealed, a club spokesman said: "West Ham United can confirm the club is making good progress in the search for a new manager and the appointment will be made by early June.
"The club is in the middle of a thorough selection process which could continue over the next 12 days before being finalised.
"The new manager will then have a month to prepare for the start of pre-season, with all at the club determined to improve on the previous campaign."
It is thought that Pompey received an approach for Grant on Thursday but the administrator Andrew Andronikou would not reveal their identity.
"I will honour the confidentiality," Andronikou said.
"We are talking about another manager's job," he told ESPN.