Chinese bike-rental firms, Mobike and Hello Transtech, expressed their willingness to enter the bidding.
It is the first time the Beijing government has penalized a bike-rental company for the number of bikes on its streets.
Beijing and Shanghai have given no indication of whether the bans will be lifted.
As the bike rental cools down, industry insiders start to ask how well the bike ban fits current circumstances.
Didi’s struggles in the bike-rental market led to a launch of its own brand, Qingju.