The northern Italian business hub is seen as the front-runner among rival bidders which include Barcelona, Bonn, Helsinki, Athens, Amsterdam and Porto.
Meanwhile eight cities, including Paris and Frankfurt, have submitted bids to host the European Banking Authority, which is also due to leave London post-Brexit, the European Council said on Tuesday.
An assessment of the bids will be published by the European Commission on 30th September, with a final decision expected in November.
The Italian government and Milan Mayor Giuseppe Sala have been lobbying hard for the city to host the EMA.
On the day after the UK voted to leave the bloc in June last year, Sala said the outcome “could be an opportunity for Milan”.
Italy's pharmaceutical industry is the second largest in Europe in terms of production, while the country is the world's number one exporter of medicines per capita.