The manager of the east London club is looking to strengthen his side as they attempt to maintain their form from the first half of the season, and as a result keep the Hammers in the Premier League.
Making it clear he is not a great fan of the imposition of a transfer window, Allardyce revealed to reporters how frantic this month is likely to be for West Ham: "I would think we would touch 1,000 [players being offered to us] by the end of January.
"I pass everything on to Martin Glover, our head of recruitment. The chairman gets a whole load of players thrown at him as well - he passes them on to us.
"At the end of the window, Martin will sit down and tot up and say we have had 1,000s of contacts probably. That's why he is panicking at the minute because he cannot get any sleep.
"It's a really difficult period for us all and we're all glad when it's over. It's been out of control since it started - it has never been under control, it has never been an ideal situation in any way, shape or form."
Allardyce is, however, well aware of the risk of making a big-money signing which fails to pay off.
"Mistakes cost you your job, don't they? Now, if I make mistakes in the transfer window and bring in players that fail, it costs me my job. It gets me the sack."
West Ham travel to Sunderland for Saturday's 3pm kick-off.