The Hammers had a reported B£3.5million bid for McCormack turned down last week and it was expected Allardyce would return with an increased offer despite Leeds' insistence that they did not want to sell the Scotland international.
"The bid for Ross was rejected on Friday and I've have spoken to Sam Allardyce since and he has said that they won't be coming back in for him," McDermott told the club's official website.
"I'm confident that he will be here after the window closes on Friday. Ross has never asked to leave. He is my captain and he is a talisman for our team.
"He scores goals and he makes them as well. He has been a good leader for the team and for me and I'm confident he will remain here.
"He has been important since April, since I turned up at the club. I'm sure that he will get better and better and will and we are going to have him for his prime years."
McCormack, 27, who joined Leeds for an undisclosed fee from Cardiff in August 2010, currently leads the Sky Bet Championship goalchart with 17.
Meanwhile, McDermott said there had been an enquiry in one of his players during the transfer window.
"There's been interest in one of the players, not Ross, and we'll see where that goes," he added.
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- Sam Allardyce