Sportsmail believes former Aston Villa manager Martin O'Neill, Steve McClaren of Wolfsburg, QPR boss Neil Warnock and Sam Allardyce, recently sacked by Blackburn, are being considered.
Time's up: West Ham have lost patience with Avram Grant (right)
West Ham would prefer to appoint a manager who requires no compensation, but O'Neill appears an ambitious target, especially with Liverpool searching for an alternative to Roy Hodgson. O'Neill would be a popular appointment for the Kop.
Grant has been told he will still be in charge of West Ham for tomorrow's third-round FA Cup clash with Barnsley, but the club have run out of patience and could even remove him today.
Ominously, his regular Friday press conference has been cancelled, due to the 'busy schedule'.
Grant, 55, is on borrowed time after losing the support of vice-chairman Karren Brady and, more recently, co-chairman David Sullivan. West Ham's other co-chairman, David Gold, remains reluctant to sack the Israeli, who is six months into a four-year contract. The trio earned a reputation for careful boardroom decisions during their stint at Birmingham.
Go-betweens yesterday made them aware that former England coach McClaren could be available, but he doesn't have great support among West Ham's board.
McClaren, who won the Dutch title with FC Twente last year, is in Marbella, Spain, working with his Wolfsburg squad during the Bundesliga mid-season break, but he is on borrowed time after a run of poor results. Grant yesterday apologised by email to West Ham fans for Wednesday night's 5-0 defeat at Newcastle.
Contender: Former England manager Steve McClaren
He said: 'I make no excuses - everything went wrong, but we must remember the form shown in four previous matches.
'Of course we are not happy with the performance and not happy with the result, but we did well before now and we will get back to that.
'It is difficult to explain what happened. It was a bad day at the office. We are disappointed to be back at the bottom but all that matters is where we are at the end of the season. I am certain we will see a positive reaction.
'I am sorry for those of you who came a long way. I am disappointed for you to see that performance after what we had given you in the previous two games. We will return to that form this week - I am certain.'
West Ham captain Matthew Upson also said sorry for his team's disastrous display in the North East.
Three and easy: Leon Best netted a hat-trick in Newcastle's 5-0 win over West Ham
The England centre back said: 'It was a fantastic effort from the supporters who came to watch and we didn't do them justice and that's a shame.
'We're obviously very disappointed and need to re-group and get ourselves together after a good run. We have put a lot of our efforts into our last four games and had good results, so perhaps this was one step too far for us because we were really poor.
'It was just a poor performance - a poor individual performance and a poor collective performance and just a poor performance from everybody associated with the team. We just have to move on.'
The 5-0 thrashing at St James' Park left West Ham a point adrift at the bottom of the Premier League, having played at least a game more than all their rivals.
Tomorrow's FA Cup clash with Championship club Barnsley is followed by the first leg of the Carling Cup semi-final against Birmingham on Tuesday night. West Ham return to Premier League action on January 15 when they host Arsenal in the evening kick-off. Defensive coach Wally Downes was brought in at the end of November to support Grant, but the Israeli now stands on the brink.
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Explore more:People: Martin O'Neill, Matthew Upson, Karren Brady, Neil Warnock, David Gold, Sam Allardyce, Roy Hodgson, Steve McClaren, David Sullivan Places: Newcastle, Birmingham, Liverpool, Spain, United Kingdom