Cole has been struggling with a hamstring injury since the end of August and Allardyce believes that the trip to the KC Stadium will come too soon for him.
There is better news for Downing, however, after the winger returned to full training with the aim of being included on Saturday.
"Joe Cole won't be available this weekend but Stewart Downing will," Allardyce said. "We're always happy to welcome players back after injury.
"From an injury point of view we're only really looking at Joe and Andy (Carroll). An extra week's training will be better for Joe
"We're glad to have Stewie (Downing) back and he'll be looking to have some game time. Guy Demel is fine and back training as well."
The 58-year-old also confirmed on Friday that Carlton Cole will be offered a short-term contract with the club.
The former Chelsea striker played 27 times for West Ham in the Premier League last season but was released at the end of the campaign.
However, he has since been training with the club in a bid to regain full fitness, and Allardyce has been impressed enough to offer him fresh terms.
"We've had Carlton training with us for a while now and as soon as he's fit enough to play there will be an offer of a short-term contract on the table there's no doubt about that," he said.
"That's why he's here with us and that's why we're trying to improve his fitness having missed pre-season.
"As soon as he's okay and suitable terms and conditions have been agreed, which is nothing do with me, then he'll join us for however long the contract is negotiated for."
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