West Ham say they will appoint “a manager who has a proven record of success at the highest level of the game” within the next seven days.
The Hammers are looking for their fourth manager since 2015 after David Moyes left the club on Wednesday.
Joint chairman David Sullivan said the Hammers had left “no stone unturned” in choosing the person they believe is the “right man to take West Ham forward”.
Sullivan added they “are now very close to reaching an agreement”.
Former Manchester City boss Manuel Pellegrini, who is managing Chinese side Hebei China Fortune, and Newcastle manager Rafael Benitez are the bookmakers’ favourites for the post.
“This is an exciting time for our football club,” Sullivan said. “We are preparing to appoint a manager who has a proven record of success at the highest level of the game.”
A West Ham statement on Thursday said the club was “extremely confident of appointing a high-calibre first-team manager, who has a proven record both in the Premier League and European football”.
Moyes replaced Slaven Bilic on a short-term contract in November with the club in the relegation zone.
He presided over nine wins and 10 draws from 31 games as the Hammers finished 13th in the Premier League, nine points clear of the drop zone.