Bochum's Yahia sustained a foot injury last week and the Bundesliga club said he would not be able to play against Egypt on November 14 at Cairo Stadium.
However, the 27-year-old, who exchanged words with Egypt and Borussia Dortmund striker Mohamed Zidan last month, vowed to take part in the anticipated clash 'no matter what'.
Bougherra, who plays for Scottish giants Rangers, is suffering from a knee injury he picked up ahead of last month's Champions League game against Romania's Unirea Urziceni.
"I'm eager to play, I haven't played regular first-team football with Algeria for a long time," ASO Chlef defender Zaoui was quoted as saying by local paper Echorouk.
"I hope Yahia and Bougherra will recover soon and play against Egypt, but if they miss out I will be ready to fill the gap."
Zaoui said Algeria would not fear playing in front of a sell-out crowd at the 74,100-seat Cairo Stadium, echoing the sentiment of several of his teammates.
Egypt players have been prohibited from talking to media by head coach Hassan Shehata.
The Pharaohs, who last reached the World Cup in 1990, need to beat Algeria by a three-goal margin to qualify directly for next year's South Africa finals.
A win by a two-goal margin will set up a playoff meeting with the Desert Foxes on a neutral venue.