Cycle development group Sustrans announced a joint initiative with the council “to boost the love of cycling in the city to Copenhagen levels”.
However, council sources said achieving that goal would require major and costly improvements - and said the authority was sticking to a far more modest target.
Sustrans is launching a “citizens’ survey”, inspired by the Danish capital, to see what residents think about cycling and highlight potential improvements.
The group said 52 per cent of people in Copenhagen cycled to work or education.
Edinburgh has one of the highest rates in Scotland, but it remains a fraction of the Danish city’s, with some 7 per cent of residents cycling to work.
The council has set a target of increasing this to 15 per cent by 2020.
Transport vice-convener Jim Orr said: “We have not set a target of reaching Copenhagen levels. We will wait until we have reached our current target.”
Sustrans said its scheme to boost cycling was also being introduced in five other British cities.
Kate Campbell, deputy director of Sustrans Scotland said: “Copenhagen and other European cities have long been held up as examples of great places to live and work, where walking and cycling is the easiest way to get around.
“Many cities in the UK are following suit and have ambitious plans to match the best in Europe.
“The adoption of a Copenhagen style citizens’ survey for the UK will help Sustrans and the cities of Birmingham, Bristol, Cardiff, Edinburgh, Manchester and Newcastle achieve those ambitions and build cities that are great for people”.