The Hammers' manager celebrates 100 games in charge at Upton Park with a replay of his first, but he will have to do so with out the former Liverpool and England pair
Both Downing and Cole are nearing full fitness following leg and hamstring injuries, but will not return in time to take on the Bluebirds in the Capital One Cup.
And Allardyce is wary of re-introducing the former England duo too early, with both sides likely to make a number of changes following the weekend's Premier League action.
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“No they won't feature in this game,” he told the club's official website. “I would have loved the match to be next week rather than this week as they both would have played.
“They won't be involved on Tuesday because both of them are only due back in training with the other players on Monday and putting them into what will be a hugely competitive game has come too early for them.
“It will be a hugely competitive match because there will be a lot of players out there who will be trying to convince both myself and Malky [Mackay] that they should be playing in the first team on a more regular basis.”
Allardyce took charge of West Ham in June 2011, with his first competitive game ending in defeat to Cardiff in the Championship, courtesy of a late winner from Kenny Miller.
Since then he has taken the Hammers back to the Premier League via the play-offs, before cementing their top-flight place with a comfortable mid-table finish last season.
“Obviously I'm very pleased with the record we had in the Barclays Premier League last year and the year before we were expected to do well in the Championship,” he said.
“We've done everything that we said we would do, not just me and the backroom staff, but also the Chairman and the Vice-Chairman and everyone else behind the scenes.
“I enjoy working in football and have enjoyed it for so many years now that it's the only thing I really know.
“When you reach 100 games and people say well done, it worries me. If it's 300 games or 400 games, fine, but 100 games should be more commonplace than it is.
“The constant change of managers which we're now faced with has turned reaching 100 games into a bit of an achievement.
“For me, that's pretty disappointing that in our professional leagues we change managers so much.”