Liverpool mayor Joe Anderson wants to ban diesel vehicles from the city centre within the next five years.
He said private diesel cars, lorries and buses could be barred from the city at certain times from 2022.
Mr Anderson aims to create a "clean air zone" by no longer licensing new diesel taxis and encouraging zero-emission vehicles.
Unite's Tommy McIntyre, who represents taxi drivers, said: "It's crazy to just bring it in without proper discussion."
Mr Anderson also suggested cruise liners docking in Liverpool should be powered by electricity so they do not have to run diesel engines in port.
The mayor's proposals will be considered by Liverpool City Council's cabinet in early June.
Mr Anderson's ideas follow those of London mayor, Sadiq Khan, who hopes all new taxis in London should be capable of zero emissions from 2018.
The Royal College of Physicians estimates that 40,000 early deaths a year can be attributed to poor air quality in the UK.
Liverpool City Council cited a Public Health England report which found 292 people aged under 19 in the city were admitted to hospital with asthma in 2014-15.
Only Manchester and Birmingham had a higher admission rate.
Mr Anderson, who is in post until 2020, said: "By 2025 I want the city to have developed a central heart where walking, cycling, electric vehicles and clean fuels will dominate, and from which polluting diesel traffic will be discouraged.
"It will also be important to introduce these changes in order to stop older, dirtier vehicles that have been banned in other cities from being relocated to Liverpool."
Liverpool-based Mr McIntyre said: "We don't oppose having eco-taxis, in fact we need them. But it will take at least 10 years, not five.
"This could really impact taxi drivers' livelihoods.
"I don't think many could afford one of these new eco-taxis."
Analysis by Claire Hamilton, political reporter, BBC Radio Merseyside
These plans were due to come, perhaps more fully formed, to the city council's cabinet in June and the idea of addressing air pollution in Liverpool will be welcomed by most. But for those who drive diesel vehicles for a living, it's causing a great deal of uncertainty.
London is being used as a comparison, as new diesel taxis there won't be granted a licence from next year. The draft plans in Liverpool suggest adopting a similar scheme.
Liverpool city centre is small and easily walkable, so it won't be hard to create a 'beating heart' for pedestrians. Cyclists, however, still bemoan the lack of provision for bikes.
A big question mark hangs over buses, although work is being done by operators to make them 'greener'. It's worth noting too, that public transport will soon come under the remit of the Metro Mayor for the city region. He or she will be elected in May.