Shaffaq Mohammed, leader of the Lib Dems in Sheffield, said following their success in the local elections last month, it was now time to deliver.
The Greens have three councillors in a new 10-strong cabinet and Labour seven.
The Star is campaigning for a return of a regular, free bus service in the city centre to compensate passengers after Pinstone Street was closed last June and stops for 27 services moved a quarter of a mile away.
The Greens and Lib Dems have supported the return of a FreeBee for several years.
Mr Mohammed said: “I expect the Greens to now deliver a FreeBee city centre bus service. It is something we have both included in our budgets for the last few years.
“They are now in a power sharing coalition so have the opportunity to deliver this much-needed bus service.”
Last week Coun Douglas Johnson, leader of the Greens in Sheffield, told The Star it would depend on likely demand.
He added: “If it can make a difference, that’s a reason to do it.”
In April, he said an electric FreeBee had been in their budget proposals for the last three years.
The service would cost £427,000-a-year, plus £1,080,000 to buy three new, electric vehicles, he added.
He said then: “More space for walking and cycling is very welcome but the move of bus stops from Pinstone Street has led to confusion for some regular bus users.
“A city centre bus would help that. Under the Green councillors' fully-costed budget proposals, a frequent electric bus would reduce air pollution, with the vehicles would be owned by the council, not a private company. It would run every 10 minutes for 12 hours a day.
“It is a very useful for older and disabled people and will complement other buses going through town. It is yet another step to help people choose to leave their cars at home.”
The traffic ban on Pinstone Street was introduced to allow social distancing and promote active travel. New stops were placed on Arundel Gate and Rockingham Street.