The move could affect 8,000 permit holders.
The council said there was growing evidence diesel engines caused heart attacks, increased lung cancer risk and reduced life expectancy.
It comes days after London introduced a Â£10 toxicity charge on the most polluting vehicles.
The dirtiest diesel bus engines will also be the first to be targeted once Glasgow city centre becomes Scotland’s first low emission zone next year, although no date for the start of restrictions has been set.
The three-month consultation as part of Edinburgh’s Parking Action Plan runs until 28 January.
Those responding are asked whether they support a diesel surcharge on residents’ and business parking permits to help tackle air pollution.
They are also asked if permits for the most polluting vehicles should be higher.
Transport convener Lesley Macinnes said: “Evidence is mounting that diesel emissions are causing serious health problems and worsening air quality in cities across the globe, and many cities are already taking steps to combat this.
“We’re keen to see what people in Edinburgh think of the idea of adding a surcharge to residents’ parking permits for diesel vehicles.
“We’ll review the consultation feedback in a report to a future transport and environment committee before deciding next steps.”
However, a motoring group criticised the proposal.
IAM RoadSmart policy and research director Neil Greig said: "This looks like a very blunt instrument to tackle poor air quality in parts of Edinburgh.
"Hard-pressed families often buy the best car they can afford and they cannot be expected to simply change their vehicle overnight and to absorb any loss of value caused by this policy.
"Diesel is still the fuel of choice for delivery, distribution and public transport, which churn out much more pollution in the city centre.
"That problem should be addressed first before measures that target private cars, which are more often a necessity rather than a luxury for Edinburgh residents."