Allardyce is already looking for additions at Sunderland.
The Black Cats boss said: “Anybody with a bit more pace, or a bit more of an eye for a goal, if you can find one at this stage of the season.
“But our judgment is that you have to be able to see him make an impact now, not two or three months down the line.”
The report says that Sunderland still have one place available in their Premier League squad, but looking for a player who is out of contract and can be registered outside of the transfer window is a pretty difficult task.
Allardyce has made a promising start to life as Sunderland manager, with a 3-0 win over fierce rivals Newcastle United lifting the side off the foot of the table.
It seems that he would like to add some more options to the side up front. Steven Fletcher showed what he is capable of with his strike on Sunday, but some would say there isn't a big man up front who is more akin to the style of play that Allardyce has built his stock on over the years, which has consistently delivered Premier League survival.
There is the issue of pace, as he has pointed out. He does have some technically sound forwards, but he does need that other option to mix things up.
He is right to say that anyone coming in has to make an instant impact, given that the side's position in the league table is still perilous, with Sunderland two points from safety.
The bedding in time for any new player would have to be minimal at best, and the same is likely to apply if the new manager wishes to bring anyone through the door during the January transfer window. He will hope, however, that by that time the situation will have improved significantly as the Black Cats look to build on their solitary Premier League win.