The move comes after a recent report by the Intergovernmental Panel on Climate Change (IPCC) showed there were only 12 years left to limit climate change.
Updated plans for how Sheffield will tackle the crisis will be discussed as a motion at a full council meeting next week.
Coun Jack Scott, cabinet member for transport and development, said: “Global warming is one of the most serious issues of the 21st century. We are facing a climate catastrophe if we don’t act.”
The council already has plans to become carbon neutral by 2050 but they are now working with partners and opposition councillors to bring the target date forward.
Jenny Carpenter, co-chair of Sheffield Climate Alliance, said: “We are delighted the council has listened to us and is now looking to take the bold step of announcing a climate emergency.
“We can all be proud that Sheffield is now the largest council to move forward in this way.”
On February 7, decision makers at City of York Council will be asked to consider a report approve a package of measures aimed at deterring stationary vehicles from idling in a bid to improve air quality and public health, and reduce greenhouse gas emissions and vehicle noise.
The recommendations include a proposal to authorise council officers to use their discretionary powers under the Road Traffic Regulations 2002 to issue £20 fixed penalty notices to drivers who refuse to switch off their engines.
If the plans are approved, a fixed penalty notice would only be issued if a vehicle has been observed idling on the public highway for more than two minutes and the driver refuses to switch their engine off.
Coun Andrew Waller, executive member for the environment, said: “Idling is an issue that we receive complaints about, particularly near schools and residential areas.”
The Government recently told Bradford Council to undertake a study to see how the city can improve air quality over the coming months.
The government will now be working with Bradford to develop a local air quality plan which sets out how it will meet the legal limits for nitrogen dioxide.
A plan must be submitted to government by October 31.
Bev Maybury, strategic director for health and wellbeing at Bradford Council, said: “I am really pleased that we are in a position where we will be planning ahead to try and alleviate the issue of air pollution in every way we can in Bradford and hopefully the health burden of air pollution can be reduced.”