Terry and Alex both missed the 3-0 home defeat by Sunderland last Sunday.
Terry has struggled all season with a nerve problem in his right leg and he travelled to Italy to see a specialist recommended by Ancelotti in midweek.
Terry is understood to be feeling slightly better but is still not pain-free enough to be considered for the trip to Birmingham.
Alex meanwhile, has postponed surgery on his knee problem in order to play against Birmingham.
When asked if he would move into the transfer market if both players were sidelined for a long spell, Ancelotti replied: "It depends what happens with Alex and in the next few days with John Terry.
"Obviously, if both players are not able to play for a long time, I think we have to think about this. But just in that case.
"There's a muscle on John's leg, the piriformis muscle, and the nerve moves, so he feels pain.
"We have to work on this problem. It's not true that he'll be out `for a month'. He went to Italy because I recommended him to go. He was the best doctor for the back and I worked with him for years.
"It depends day-by-day with John. He has pain. He will not be involved tomorrow but, maybe, he'll be able to play in the next game. We're not satisfied, but we hope we'll be able to put John in the condition to play.
"I don't remember how many times I was 100% fit when I played. You often have problems.
"Alex will be available, which is good news. He trained well for the Brazilian team. We know he needs surgery, but we can procrastinate for this. There's no risk, but his knee needs to be clean.
"It will be good to have him back. We didn't play well last week, played a poor game. It was the first time in my period here, so we need to move on immediately and have a reaction.
"The reaction will not be because we have got Alex back. We'll have a reaction if everyone works for the team, works hard and shows a good mental attitude and fighting spirit.
"Our aim is to play well, better than we did against Sunderland. We want to forget Sunderland with a fantastic performance.
"If we play well, we can win and maintain our position at the top of the table." Ancelotti will also have his new assistant first-team coach Michael Emenalo in tow against City.
Birmingham could restore Lee Bowyer to the starting line-up.
Craig Gardner is struggling with an ankle injury, which he suffered against Manchester City, and Bowyer is standing by to take his place.
Manager Alex McLeish will examine a specialist's report before deciding whether to play former Aston Villa midfielder Gardner. McLeish was awaiting the return of a number of his international players before deciding on their fitness.
McLeish believes his team can add to Chelsea's troubles by beating the champions.
McLeish acknowledges Chelsea have strong players to come in for their injured stars, but claims his team feel they can pull off a surprise.
The former Scotland manager said: "The big teams don't lose too many in succession, but we're in our own back yard, and we have to believe that this is achievable and we can win it.
"I'm not saying that we will do it, but we can do it.
"We've got to ensure that Chelsea are going back to London on the coach saying, 'St Andrew's is a tough place to go to'.
"We did that with a lot of the big teams last season, but we were unlucky against Chelsea when Chucho (Benitez) scored a perfectly legitimate goal which was ruled out.
"Chelsea have got some injury problems, but they still have phenomenal players in the squad who can easily turn it on when they want."
McLeish hopes his players are able to capitalise on any doubt that might manifest itself in Chelsea's play.
"They're only human, and players can be apprehensive from time to time," McLeish said.
"When the confidence is high, there's no stopping footballers, but when the chips are down a wee bit you can feel that apprehension.
"If there's a opportunity for us then we have to try and grasp it.
"We've got to gather points for very different reasons, but it's a great challenge for us."