The combined authority issued a statement on Wednesday evening, with bosses raising 'fundamental' concerns over the level of Government funding being provided.
They say that more money is needed for taxis, vans, minibuses and coaches.
In a statement, Chief Executive of Greater Manchester Combined Authority, Eamonn Boylan said that they are seeking approval from the secretary of state for an "urgent" review into the launch of the Clean Air Zone to "identify how a revised policy can be agreed to deal with the supply issues and local businesses’ ability to comply with the plan".
What is the Clean Air Zone?
Commercial and passenger vehicles deemed as 'most polluting' will have to pay a daily charge to travel in the Zone, which will come into force from 30 May 2022.
It is hoped it will reduce nitrogen dioxide air pollution at the roadside, bringing it down to within legal limits.
It will cover all 10 boroughs of Greater Manchester - an area of around 493 square miles - which would be the largest scheme of its kind in the country.
Eamonn Boylan said that in March 2020, the government issued a legal direction requiring the ten Greater Manchester local authorities to address the vehicle pollution problem by introducing a Category C charging clean air zone.
Greater Manchester was offered £120 million to support people in upgrading their vehicles to become compliant with the new rules, but "emerging evidence" from local businesses suggest that the funding may not be sufficient, and could cause them to collapse.
More than 33,000 people have signed a petition against the proposed introduction of the CAZ. The plans have seen major opposition from people across the region who face having to pay the charge - but some environmentalists believe it does not go far enough.
In the statement Mr Boylan said: "There is a fundamental concern whether the current financial support package agreed with government – including nearly £100m of funds due to open at the end of January for light goods vehicles, minibuses, coaches and taxis and private hire vehicles – is sufficient."
The Greater Manchester Air Quality Administration Committee is set to meet on January 20 to discuss the current government funding schemes.