City boss Roberto Mancini is preparing to ring the changes for the Hawthorns clash.
Mancini indicated in the wake of City's 2-0 Premier League win at Wigan on Sunday that he would be prepared to let Given leave in January, with Joe Hart having nailed down the number one spot.
And, although he would not be drawn on Given's possible participation at The Hawthorns, Mancini stressed the importance of rotating his squad as injuries and a heavy fixture schedule begin to take their toll.
Emmanuel Adebayor, Jerome Boateng and Roque Santa Cruz all missed the trip to the DW Stadium and Mancini insisted: "Every game is important for us this season and it is important the players understand the situation.
"We can't leave one competition. We must play at 100% in every competition and that means in the Carling Cup we must change some players - because we can't play every two days."
Mancini also hopes squad rotation will help build the belief among his wider squad after City once again had to rely heavily on the influence of Carlos Tevez to get past the Latics.
Tevez scored one and set up City's second for Yaya Toure, and both goalscorers can expect to be left on the sidelines as Mancini experiments with alternatives without his two most in-form stars.
Mancini added: "If we want to win something we must understand that we can also play without Carlos and Yaya. They are fantastic players but we must also be a team when we are missing them.
"If we don't do that then we will not improve. At the moment we have a problem because we are missing four or five players but when all the players are back it is important we play some games without them."
Meanwhile, Mancini denied suggestions that Given's freshly-stated desire to leave Eastlands stemmed from last Thursday's Europa League trip to Salzburg, when the keeper was under the impression he would play.
"I never said to Shay that he would play on Thursday," added Mancini. "The goalkeeper is a particular situation because I cannot play two of them. At the moment Joe Hart is playing so Shay must stay on the bench."