The former Chelsea striker had attracted interest from a number of Premier League clubs having fallen out with officials at current outfit Shanghai Shenhua.
Allardyce had previously stated that the Frenchman's wage demands may rule out a deal between the two parties, but now the Hammers boss has denied Anelka moving to Upton Park altogether.
"At the moment I am not in a position for Nicolas Anelka because my main priority is defenders," Allardyce said.
"We have got Andy Carroll close to coming back and we have got Carlton Cole, Marouane Chamakh and we have also brought in Wellington Paulista."
West Ham face another one of Anelka's old clubs Arsenal on Wednesday.