Rail formed part of the city's plans to create an integrated public transport system, with buses and minibus taxis, councillor Brett Herron said.
He said Transport Minister S'bu Ndebele approved the city's proposal to manage passenger rail in December, in order to better integrate all forms of public transport.
"It is extremely important for the city and for our residents that there is a substantial improvement in the quality, frequency, reliability and safety of this (rail) service," Herron said.
The city should be given full management authority, along with the rail subsidy, to plan, manage and fund the service.
Still under discussion
Prasa spokesperson Nana Zenani said the matter was still under discussion.
"There has not been an agreement," she said.
The transport department was not immediately available for comment.
On Monday, Beeld newspaper reported that the government was considering handing control of passenger train services from Prasa to cities.
Deputy Transport Minister Jeremy Cronin said the government wanted cities to develop a comprehensive transport system, taking into account buses, trains, minibus taxis and other means of transport.
"Our cities are expanding at an ever accelerating pace. The government expects that by 2030, 70% of South Africans will be living in cities, and it is therefore important to develop systems that can keep pace with this level of growth," he reportedly said.
Public transport should be integrated with the development of settlements and industries.
Currently, cities were responsible for city planning, but had no control over metro train services, which complicated co-ordination.
Cronin said Metrorail passenger services formed an integral part of city infrastructure.
Thus far, Cape Town and Durban's systems looked as though they would be the easiest to transfer from Metrorail to city authorities.
The government was still discussing the financial and logistical details with Prasa, Cronin said.