Carlo Ancelotti's Barclays Premier League leaders have lost two of their last three matches, the most recent defeat a 3-0 drubbing at home against Sunderland. They will also be without key players John Terry, Alex and Frank Lampard for this weekend's clash.
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."