Heskey has been sidelined since injuring his ankle in the game with Blackburn Rovers whilst Koumas has inexplicably not played during the Steve Bruce era.
The club have now confirmed that the former Tranmere and West Brom player has been suffering from a hamstring injury picked up in training two weeks ago.
Both players are touch-and-go for Wednesday. Bruce told the club's official website: "The good news is that both Jason and Emile are training today [New Year's Eve], and the addition of those two players in my plans are a terrific boost. We will make a judgement on both on Wednesday."
The trip to Liverpool will not be easy and Bruce realises this. He does however have a good record against the scousers and will be hoping to pick up something from the trip.
Bruce added: "When you go to a place like Anfield, you need to be at your best to get something, and it's always a massive occasion for any club to visit there.
"Touch wood, I've enjoyed a reasonable record there in the past, and against Liverpool in general, but to get something Anfield would be a great achievement. We will go there full of confidence, and approach the game in the same way as we would any other."