A motion has been tabled for discussion at a council meeting later this month.
Labour's transport spokesman Ross Grant claimed operators had reneged on running services to some communities.
However First, which operates many city services, said councils and operators had to work together to unlock potential.
Mr Grant said the council could learn from colleagues in Edinburgh, where the authority part-owns its own bus fleet.
However, Aberdeen's SNP group leader Stephen Flynn said it could cost millions of pounds each and every year.
The Labour group on Aberdeen City Council is calling for all options to be explored to allow the local authority to run its own bus company.