The party updated its members on the situation following a week of formal talks with Sheffield Liberal Democrat and Green Party leaders.
They have been discussing a way forward after the council was pushed to no overall control at the local elections last week.
Labour lost eight seats, five to the Green Party and three to the Liberal Democrats making the overall numbers of seats 41 for Labour, 29 for Liberal Democrats, 13 for the Green Party and one for the Conservatives.
Councillors Terry Fox, leader of Sheffield Labour, and Julie Grocutt, deputy leader, said: “We believe that Sheffield’s interests must always come ahead of party politics, and as largest the political grouping on the council is incumbent on us to find a way forward.
“It is essential that as the city comes out of the pandemic, and continues to rebuild, that the council is not bogged down by political deadlock. Fundamentally we need to find a solution which puts Sheffield first and find a way of councillors pulling together for the benefit of the city.”
They said one of their main principles was changing the council to a committee system as soon as possible.
This follows a governance referendum which saw 64.8 per cent of voters choose to change from a strong leader and cabinet model to a modern committee system.
It does not have to be implemented until May 2022 but Labour said no overall control presented an “ideal opportunity” to trial a new way of working.
They also said they want political proportionality across everything, including the council executive, also known as cabinet – saying it is the “fairest way forward”.
The Green Party went into the talks calling for a rainbow cabinet that would see all three parties share control.
Coun Douglas Johnson, leader of the party, said: “If anything, the message from the (governance) referendum is that parties have got to work together so we are proposing that we should do. It’s the best way to do something when, in a lot of cases, people of all parties actually agree with each other more or less on most things.
“The current system creates artificial divides which allows exploitation of issues for party purposes really, so getting people to work together in a way that is much more to do with cooperative and collaborative approach to running the council.”
Liberal Democrats said their priority was the “people of Sheffield and future opportunities” and that they would be happy to work with any party on the council who sign up to that priority and work to implement policies they see as vital for Sheffield including an independent inquiry into the street tree felling saga and committing to Arup’s pathway to carbon zero by 2030.
Coun Fox and Grocutt said talks are still on-going but they said it will not be left to “handshake agreements” and citizens will know publicly about whatever agreement is reached.