The proposed ordinance was one of then-candidate Kristen Brown's most prominent campaign promises.
The purchase, if it happens, would be nearly equal to a fifth of the company's total stock value.
Despite a city council vote of 4-2 for the ban, some residents say they are not pleased.
Arlette Cooper-Tinsley is one of the few people to have held leadership posts in both Fred Armstrong and Kristen Brown's regimes.
The Columbus ordinance is stricter than the state smoking ban that provides exemptions for bars, taverns and private clubs.
After tabling the measure last month, the council will likely vote on the smoking ban Tuesday.
Hostess Brands announced Friday it is going out of business after strikers did not return to work Thursday.
Cummins plans to lay off 1,500 employees across its entire workforce by the end of the year.
Hostess employees have been on strike for nearly a week at a plant in Columbus.
Cummins recently announced a drop in quarterly profits and plans to lay off more than 1,000 employees, which could have ripple effect in the Columbus community.