West Ham hope to appoint their new manager by the end of next week, BBC Sport understands.
Reports suggest former Blackburn, Newcastle and Bolton boss Sam Allardyce is in the frame to succeed Avram Grant.
West Ham sacked Israeli Grant after they were relegated from the Premier League with one game remaining.
Caretaker manager Kevin Keen, who took charge for that game, a 3-0 home defeat by Sunderland, has stated his desire to lead the Hammers in the Championship.
However, Keen has no formal managerial experience, apart from looking after West Ham's reserve team.
Allardyce was surprisingly sacked from his role as Blackburn manager in December after three defeats in five games, with Rovers 13th in the Premier League, five points above the relegation zone.
The Lancashire club slipped deeper into the relegation battle following Allardyce's exit and only guaranteed another season in the top flight by beating Wolves 3-2 at Molineux on the final day of the season.
Other managers who have been linked with the vacant post include Chris Hughton and Paul Lambert.
Why on earth would Big Sam accept the West Ham job?