Liverpool City Council hopes the measure will help halt the worrying rise of skin cancer - the fastest growing cancer among 18 to 35-year-olds in the UK.
The Look To Die For campaign, which launches today, is proposing all premises offering the use of sunbeds should be compelled by law to provide clear information about the serious health dangers associated with their use.
Licensing would ensure that a number of minimum health, safety and good practice guidelines are met in all facilities offering the use of sunbeds.
The initiative, supported by Cancer Research UK and the Liverpool Clinical Commissioning Group, is also aiming to reduce the number of teenage girls in the city using sunbeds.
Cancer Research UK said using a sunbed just once a month or more will double the chance of developing malignant melanoma - the most serious form of skin cancer.
According to a study carried out by the charity, 40% of sunbed users aged 11 to 17 in the city said they are using them at least once a week to perfect the "Liverpool Look".
In England, only Nottinghamshire and London are able to license sunbed businesses to ensure that they take steps to protect the health of their customers, but cities like Liverpool are unable to do this.
Roy Gladden, assistant cabinet member for adult health and social care and cancer champion for Liverpool City Council, said: "Liverpool has a significant problem with sunbed use compared to many other parts of the country. With 'The Look To Die For' we are putting forward a strong case to the secretary of state to grant local authorities the powers they need to protect their constituents.
"The link to skin cancer from sunbeds is well documented and we just want to ensure that everyone in England, no matter where you live, has the right to know the risks of using sunbeds so that they can make an informed choice about using them."
The campaign's petition can be found at: www.thelooktodiefor.co.uk/petition.