The 89-year-old has never hidden his wish to step down before the expiry of his seven-year term because of his age and state of health but on Tuesday said he would stay in office until Italy's presidency of the European Union expires.
This would end on January 13th and Italian media say Napolitano, who has served as president for more than eight years, will step down on January 14th or 15th.
In 2013, Napolitano reluctantly agreed to a second term due to a political crisis stemming from deadlocked elections earlier that year.
The Italian president is elected by parliament and has broad powers which include appointing the prime minister. The head of state can also dissolve parliament and call snap elections.
Once Napolitano steps down, the parliament has to meet within 15 days along with 58 regional deputies to choose a new president.
The winning candidate has to have a two-thirds majority in the first three rounds but only a simple majority is necessary from the fourth round onwards.