The proposals have been backed by environmental campaigners but opposed by Scottish Labour and business groups.
They would see employers paying an annual levy on every parking space at their premises, which they could pass onto staff and visitors.
The money raised would be ring fenced for improving public transport, cycling and walking.
The scheme would not cover shopping centres or retail parks, but councils could choose to include schools, colleges and universities.
Other exemptions include blue badge holders’ spaces, those for healthcare workers at hospitals, and parking at hospices.
Local authorities interested in launching a scheme would have to conduct a further consultation themselves.
The only UK scheme launched so far was established in Nottingham in 2012, which charges £428 a year per space.
It has been regarded as successful in raising tens of millions of pounds from tram, rail and bus improvements.
Mr Dey said: “It has never been more important to take decisive action to tackle climate change - and Scotland is leading the way by committing to reduce the number of kilometres travelled by car by 20 per cent by 2030.
“Workplace parking licensing has the potential to be a key tool for local authorities to help us reach this ambitious goal, by encouraging the use of more sustainable travel modes, reducing congestion and tackling harmful emissions.
“As the net revenue generated must be committed to support policies in local transport strategies, this policy is also intended to finance improvements in public or active transport, making it more attractive and thus encouraging individuals to leave their cars at home.”
A Glasgow City Council spokeswoman said: “We continue to explore workplace parking levies as one potential element of the city’s developing transport-related strategies. which, alongside other measures, can support and improve sustainable travel in our city and play a part in Glasgow’s efforts to achieve carbon neutrality by 2030.”
A City of Edinburgh Council spokesperson said: “It’s important we look at all the tools available to us to help make Edinburgh a more sustainable, environmentally-friendly city, and to support our goal of becoming carbon neutral by 2030.”
The Scottish Government’s Transport Scotland agency said under the scheme, employers would have to get a licence from the council for each workplace parking place provided for staff and “certain visitors such as workers, agents, suppliers, business customers and business visitors”.
It added: “Parking places occupied by someone attending a course of education or training and parking places occupied by members of bodies whose affairs are controlled by its members may also require to be licensed.
"Parking places used by non-business customers would not be liable for the charge: for example, customer parking places at a supermarket or shopping centre would not need to be licensed.”