The public consultation, which opened on Wednesday, particularly seeks contributions from residents and visitors to the Scottish capital, as well as businesses, investors and the hospitality and tourism industry.
Edinburgh City Council is looking at bringing in a transient visitor levy (TVL) with draft proposals suggesting those visiting the city pay £2 a night, or 2% extra on the overall cost of their room, year round, capped at seven nights.
Research suggests this could bring between £11 million and £13 million annually to the city.
If the plan is successful, Edinburgh could become the first place in the UK to introduce the levy, following in the footsteps of cities such as Paris and Barcelona.
Respondents to the online consultation are being asked to give their views on the details of the proposed tax and what the money raised should be spent on.
Current government policy does not support a tax but Ms Sturgeon said all sides would be listened to.
Any plans to introduce the levy in Edinburgh would need the support of the Scottish Government to proceed.
Edinburgh City Council leader Adam McVey said: “The First Minister’s announcement was welcome in that their work will provide a national context for our proposals, adding to the detailed engagement we have already carried out as well as the citywide public consultation we are embarking upon today.
“We have always acknowledged the need for legislation in taking this forward but we as a council have also maintained the need to develop our own plans to make sure it’s not just any TVL but the right TVL for Edinburgh, taking account of our local circumstances.
“Our plans have been developed through engagement with the industry and we see this consultation, alongside the Scottish Government’s, as a way of further co-producing a scheme that works best for the city and our stakeholders.
“We are very much listening to everyone involved around what they believe is a fair, simple and workable policy.”
The council consultation will last for eight weeks.