The list includes some of Italy's lesser-known sites, such as the Ancient Roman ruins of Ostia Antica, Emperor Hadrian's summer villa at Tivoli and Rome's National Etruscan Museum.
The new directors will be charged with “helping them become lively and inclusive places capable of promoting cultural development.”
The call for applicants is the second phase of a government plan to make Italy's museums – which boast some of the greatest archaeological remains and most iconic pieces of art in the western world – more competitive.
An international recruitment drive last year saw the Italian government appoint seven foreign directors at some of the country's biggest museums in a bid to boost visitor numbers.
In spite of the cultural riches Italy owns, not one Italian museum is in the top ten globally in terms of visitors.
Florence's Uffizi art gallery pulls in just 1.5 million visitors each year, a fraction of the 8.5 million who visit the Louvre gallery in Paris each year.
“This new international call will capture the attention of the global scientific community,” said Italy's Culture Minister Dario Franceschini. “By the end of the year, another nine jewels will have new directors – chosen from leading global experts.”
In order to land the job, candidates will need to be educated to at least M.A level, have publications to their name, speak Italian and have experience managing cultural sites.
The four-year roles pay €78,000 a year, plus bonuses.
Applicants have until July 20th 2016 to apply. More information can be found on the Culture Ministry's website.