Injuries to key first-team players have seriously hampered the Hammers so far this campaign, with the 3-1 Boxing Day defeat to Arsenal leaving them in the Barclays Premier League relegation zone.
Co-chairman David Sullivan has publicly promised funds for additions next month, and Hammers boss Allardyce would like nothing more than to sign another Djorkaeff.
The World Cup-winning forward's career was winding down when he joined up with Allardyce at Bolton in 2002, yet his class proved just the tonic as the Trotters avoided the drop.
"I can't tell you exactly when Andy Carroll will be back," the 59-year-old said when asked about injuries. "I am not medically qualified enough to say.
"Winston Reid, Stewart Downing, Ricardo Vaz Te, James Collins and Ravel Morrison have all got to get fit as quickly as we possibly can.
"If we have got two additions in January, my concern is to make sure they can hit the ground running.
"I need them to jump into the team and deliver what we know he has delivered elsewhere from day one. That is a massive, massive task in this window, but we have to try and achieve it.
"It would help if they had Premier League experience, but you have to take the CV of a player if they are from abroad, if he is a top, top player in the countries he has played, like a Djorkaeff.
"He kept me up at Bolton many, many years ago when I was in this position. He came in January, scored the goals we needed, kept us in the division with two or three games to go.
"A player with an impact like that would be important not just for the team and the results, but everybody at the club."
Source : PA