Bach said that the International Olympic Committee is prepared to withdraw recognition of the Indian Olympic Association if it fails to adopt "rules of good governance" by Tuesday.
The Indian body, which is already under suspension due to government interference, is due to meet Sunday to consider the IOC's ultimatum.
Bach said, if there is no breakthrough, the IOC executive board can recommend the ultimate sanction - "de-recognition" of the Indian association.
It would be the first time a country has been kicked out of the Olympic movement since South Africa was expelled during the apartheid era.
"We will see if there is any last-moment movement," Bach said. "If not, then we have to consider to take the next step."
The IOC suspended the Indian body a year ago because of government interference in its election process.
While many of the issues have been resolved since then, the Indians have yet to agree to the IOC demand to bar officials who have been charged with a criminal offence - an impasse which has led to the final ultimatum.