Klaasen sat out of the ICC Champions Trophy opener against Afghanistan, "as a precautionary measure due to a left elbow soft tissue injury," according to a brief statement from Cricket South Africa released last Friday.
Whether he will be ready and available for selection against the Ausies on Tuesday remains unclear, as Bavuma refused to give much away in his pre-match briefing.
"Well, I mean, they still have to assess his fitness – there's obviously still the practice today so he'll do his practice today," Bavuma said.
"Mainly he is batting and I guess him and the medical team they'll make a decision accordingly."
Meanwhile, with Australia without frontline bowlers Pat Cummins, Josh Hazelwood and Mitchell Starc, the South African skipper assured they will not take the challenge lightly on what clearly are batter-friendly surfaces in Pakistan.
"I mean any Australian outfit that comes together for an ICC event is always one that you don't take lightly. Yes, they don't have, I guess, their mainstay bowling attack, but I think they still have enough to be successful as a team," he added.
"Like you mentioned, with their batting maybe it could be a case of their batters maybe doing a little bit more than what they're accustomed to, so I think, like with any team, there are opportunities and probably within the bowling there's opportunities.
"And I think, if that presents itself on the day, we'll definitely be looking to make use of that opportunity, but, in saying that, we definitely won't be taking them lightly."