The Scottish Government has already announced Glasgow will get the first experimental LEZ, allowing it to ban the vehicles with the worst emissions from a designated area of the city.
But ministers have also said Edinburgh, Aberdeen and Dundee will have LEZs by 2020.
Cllr McVey said plans were being drawn up on how Edinburgh’s zone could be developed.
“In the next six months we will see a lot more flesh on the bones,” he said.
Just last week, St John’s Road in Corstorphine – frequently labelled Scotland’s most polluted street – was second on Friends of the Earth’s list of hotspots for nitrogen dioxide after Glasgow’s Hope Street. The Capital’s Queensferry Road was number six.
And the environmental group’s parallel list of the worst streets for particulate matter had Leith’s Salamander Street in top slot, followed by Queensferry Road, with Glasgow Road, Corstorphine, at number five.
Cllr McVey said work had been carried out, such as changing traffic light sequences to avoid queuing vehicles, and had shown it was possible to make improvements.
But he said: “The LEZ is hugely important because it takes it to the next level and gives us the ability to take areas which have the most acute problems and take the most polluting vehicles off these routes.”
He said discussions were still needed on the extent of the LEZ and exactly which vehicles would be affected.
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“The starting point is for the widest possible area because obviously a big concern is displacement,” he said.
“What we don’t want to do is send some of the heaviest, largest and most polluting vehicles driven down some of our smallest, most residential streets.”
Whether the worst-polluting cars would be included from the start along with lorries and buses was also yet to be decided.
But he said some issues were likely to be covered by national guidelines expected to be issued by the Scottish Government to ensure a consistent approach across the country.