Green party councillors want Sheffield to join the Yorkshire-wide devolution campaign.
The group will put forward a motion at today's full council meeting urging the ruling Labour group to join the 'coalition of the willing' and seek a Yorkshire deal from the Government, rather than focusing on South Yorkshire.
The decision by Barnsley and Doncaster councils to pull out last month has thrown the future of the £900 million Sheffield City Region deal into doubt. But the Government has insisted a mayoral election will take place next month as planned. An 'in principal' deal to hand over powers was signed in 2015.
The poll would cost about £1 million to stage but would leave the city region mayor with few real powers.
The Greens' motion, put forward by Coun Rob Murphy, says the council should 'should stop following this Government's agenda on devolution and listen instead to the views of the people of Sheffield'.
Coun Murphy highlights a 2012 referendum in which Sheffield voted 65 per cent against the idea of an elected mayor for the city.
He blames the failure of the South Yorkshire deal on 'poor leadership across the region'.
And he adds that a final decision on devolution for Yorkshire 'should not be made without a Yorkshire-wide referendum'.
The Liberal Democrats will also use this afternoon's meeting to talk about devolution. But the party's councillors will urge their Labour colleagues to work with South Yorkshire authorities.
Coun Shaffaq Mohammed will push for a 'way forward for the Sheffield deal that accommodates all South Yorkshire partners'.
He will express concern at the potential for an elected mayor with 'very limited powers', and that the 'recent break down in trust within South Yorkshire potentially puts at risk jobs and future investment in our local area'.
And he will ask the council to suggest that 'to keep the prized devolution deal on the table, local politicians and Sheffield City Council now needs to focus on how to go forward and not blame other Councils for the impasse that we find ourselves in'.
Last month council leader Julie Dore said she would move forward with 'positivity and ambition' following the collapse of the city region deal.
“We have stuck to our word throughout this and shown that Sheffield is a place where you can do business," she said.
"Sadly it seems Barnsley and Doncaster have burned their bridges."