The Queensland state capital is mulling whether it can justify the expense of hosting such a major event, and has carried out feasibility studies which Bach viewed during a visit.
"I must say that we have been impressed to see how detailed the feasibility studies are already at this early stage and how well founded these studies are," he told reporters.
"Now it is up to the Australians to make their minds up, and to say whether they want to follow up on this project to host the Olympic Games."
With the next two Olympics in Europe and North America, the 2032 showpiece is expected to take place in the Asia-Pacific region.
So far Jakarta, which hosted the last Asian Games, has applied and Mumbai has expressed interest, while the IOC has also suggested a joint bid by the two Koreas.
Bach said it was encouraging to see the interest given 2024 host Paris and Los Angeles in 2028 were selected unopposed, with a healthy slate of candidates for 2032 seen as necessary to restore faith in the process.
"For us at the IOC, this is first of all very encouraging that already now we have a number of cities who are interested in organising these 2032 Olympic Games," he said.
"It shows the growing attractiveness of the Olympic Games, worldwide and for the host cities."
Brisbane mayor Adrian Schrinner said discussions with the IOC had been "very positive".
"We will be talking to everyone, it is important to have support through the whole political spectrum," he said.
The IOC is not due to select the host until 2025.