The London outfit are also into the fourth round of the FA Cup after beating Everton in a thrilling third-round replay on Tuesday evening to set up a tie with Bristol City.
That will mean extra pressure on the West Ham squad, with January the perfect time to add additions and push towards European qualification or a potential FA Cup run.
However, Allardyce has suggested it is unlikely that his side will be making any moves, unless a player of a certain calibre is available.
“There’s been nobody available at the moment,” Allardyce told Sky Sports.
“I think with what money we do have available is only wages, so if a player pops up within that wage structure, and we feel it’s somebody who could have an impact immediately on the team, then we will pursue it.”
The manager did, however, admit that the January window can have surprises as teams use it to assess their squads and strengthen ahead of the of the second part of the season.
“However, I think that [any signing] is highly unlikely in this window, but you never know what turns up in the next two weeks so we will never say never, but probably unlikely,” he added.