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McDonald, who had a spell in charge at Brunton Park from 2006 to 2007, was among the frontrunners to take over the League Two strugglers, but has instead opted to remain with the Hammers.
‘Obviously there has been a lot of speculation about Neil McDonald, and I think it's only fair to say that he has formally withdrawn his name from the process and we respect that decision totally,’ Carlisle managing director John Nixon told the club’s official website.
‘That has made a difference to the shortlist because he was a strong candidate as far as we were concerned.
‘He's given it a great deal of thought over the last five to 10 days and he has spoken to us about the situation.
‘He has told us that he has discussed it with his family, having thought about it long and hard, and he has decided that it isn't the right career move for him to make at this point in time.’
There could still be a West Ham-related appointment at Carlisle, however, with former Hammers midfielder and ex-Milwall boss Steve Lomas one of the names linked to the job over the past two weeks.
Elsewhere, another former West Ham midfielder could be about to end his long-running search for a new club, with Jack Collison offered a short-term contract at Ipswich Town.
The Welsh midfielder, who left the London club this summer after making 121 appearances over seven seasons, has been in training with Town, as well as with Championships rivals Birmingham, and his now weighing up his options.
‘I offered him exactly the same as Darren Ambrose, to January, and I've told him that offer still stands,’ manager Mick McCarthy told the East Anglian Daily Times.
‘Things all seem sweet now but we get to November and suddenly we've got a flu epidemic and we've people with injuries and suspensions so another body of that quality would be nice.’