The EMA is in charge of approving drugs in the union and currently employs around 900 people at its headquarters in London's Canary Wharf, with a budget of around three billion kronor ($338 million).
With the UK set to leave the EU, several countries including Sweden, Ireland, Italy, Malta, Hungary and Austria have expressed their interest in hosting the authority.
The Swedish government has now tasked Stockholm's county administrative board with the job of promoting the city as a new base. It has been asked to prepare information on "what the EMA can be offered in terms of communications, housing and proximity to medical research," according to Sweden’s Ministry of Health and Social affairs (Socialdepartementet) in a press release.
In July, the EMA's Swedish former director said that hosting the agency would help Sweden appeal to companies and provide funds for research and development.
But the fact that the EU's disease authority, the European Centre for Disease Prevention and Control, is already based in Sweden could be a problem.
"Many countries have no EU agencies based there at all, so the odds may not be the best," Thomas Lönngren told Sveriges Radio.