Conservative MSP Miles Briggs said the capital has become "overheated like London" and the situation is getting "worse and worse".
He called for discussions around London-style pay weighting in the city, with an initial focus on key sectors such as social care.
He said: "The problem has been building over decades now. I think it is time we got a proper solution for Edinburgh."
The City of Edinburgh Council said it is "determined to convince more employers in the city to increase wages" and become living wage accredited.
Recent figures show the price of renting a one bedroom property in the capital has risen by almost half in the last decade.
Meanwhile, Edinburgh's delayed discharge rate in hospitals is the highest in Scotland, partly due to shortages in the care sector.
Mr Briggs said he is keen to speak to SNP Finance Secretary Kate Forbes about the issue as well as holding cross-party discussions.
He said: "I hope we can have a discussion around maybe an Edinburgh weighting being developed, because things are just getting worse and worse and the cost of living issues in the capital are going through the roof."
The Lothian MSP added: "A couple of organisations I've been speaking to are starting to say they think that's where we'll have to go.”
Mr Briggs said discussion around a city-specific rate of pay "probably needs to start with areas where there is a crisis” such as social care.
He added: "I think the thing is, probably all boats need to rise around this in Edinburgh.
"But I've been trying to push specifically around social care, because everything is at crisis point around that at the minute."
Mr Briggs, who is the Tory spokesman for social justice, said efforts to make terms and conditions and pay better in social care had to be more “innovative and imaginative”.
He added: "I personally think we should start with social care and see if that works, then I think a lot of sectors will soon want to see something similar."
Most London employers pay staff extra due to the cost of living. The independently-calculated real living wage is £11.05 per hour, compared to £9.90 in the rest of the UK.
Kate Campbell, Edinburgh Council’s fair work convener, said: “As a newly accredited Living Wage City we are determined to convince more employers in the city to increase wages, demonstrating they value their staff and fair work practices by becoming living wage accredited. Given that many people working on low wages are in the private sector, we believe this is the right approach to make our city fairer for everyone.
“As part of our action plan we have set targets by sector, and we will be working to encourage businesses in various sectors not already credited to become part of the scheme by pointing out the benefits for staff and businesses of doing so. This includes the care sector, although we recognise that there are many employers in the care sector that already pay the living wage as a minimum but may not be officially accredited.”
A Scottish Government spokesman said employment law is reserved to the UK Government.
GMB Scotland senior organiser Keir Greenaway said the union would look at the idea "with interest", but stressed there is a national problem in social care.
He said: "If there was an Edinburgh rating, it would need to come with national measures as well to fix the underfunding crisis."