The term of the current president ends in April 2019 but the discussion has started over a potential successor or even the possibility of extending the current term.
The President is nominated by the prime minister, and although talks are sometimes held with the Opposition, agreement has been rare. The President is appointed by a simple majority of the House. A second term would only be possible with an amendment to the Constitution, which would require a two-thirds parliamentary majority and therefore an agreement with the Opposition.
All of Malta's Presidents so far have been former politicians with the exception of Sir Anthony Mamo, who previously served as Chief Justice and then Governor-General.
Marie-Louise Coleiro Preca's term ends in April 2019.One president, Eddie Fenech Adami, was a former prime minister.
Four - Anton Buttiġieġ, Ċensu Tabone, Guido de Marco and George Abela were deputy leaders of their political parties.
The other presidents - Agatha Barbara, Ugo Mifsud Bonnici and Marie-Louise Coleiro Preca, served as ministers.
Former Labour deputy leader George Vella is among the names being mooted for the post of President of the the Republic, though Ms Coleiro Preca is seen by many as an ideal compromise president, should there be agreement on extending her term.
Other names that have been mentioned for the post include former MPs Joe Micallef Stafrace and Joe Brincat.
Should Prime Minister Joseph Muscat emulate his predecessor Lawrence Gonzi and appoint a prominent official from the opposing party? Or should Malta opt for an outstanding personality like a former civil servant, or perhaps the long-serving head of an NGO?
Tell us who you think should be appointed as Malta's new head of state, and the reason why in the comments section below.