Beijing and Shanghai have given no indication of whether the bans will be lifted.
Other bike-rental companies are considering raising prices, as warmer weather brings a likely rebound in trip numbers.
Chinese bike-rental firms, Mobike and Hello Transtech, expressed their willingness to enter the bidding.
The law comes as concern mounts about the financial stability of a number of mobility firms in the rental economy sector.
All of China’s most visible mobility players have undergone significant change over the last 12 months.
Didi hopes new strategies will help it complete a U-turn that will get it out of the dead-end in which it finds itself.