Gentilini - an Italian, as is EU foreign policy chief Federica Mogherini - currently heads the EU's Western Balkans and Turkey division and his appointment will have to be confirmed by member states.
The Middle East position was created in 1996 after the Oslo Accords offered the prospect of real progress towards a Israel-Palestinian peace deal.
Mogherini's predecessor, Briton Catherine Ashton, abolished the office in a controversial move aimed at bringing the European Union's peace efforts under one roof in its external affairs arm.
The EU also plays a prominent role in what is known as the Middle East Quartet, set up in 2000 by the UN, the EU, the United States and Russia to promote peace efforts but which has also become bogged down.
Former British prime minister Tony Blair is the Quartet's special envoy and Mogherini was asked on Monday about reports that he was scaling back his role.
She said foreign ministers had not discussed Blair's position but did talk about "how to revive the role of the Quartet".
"We discussed the future of the Quartet initiative. Blair's responsibility is to focus on economic development (of the Palestinian territories) and that is not the focus at the moment which is on relaunching the peace process," she said.
The EU has been dismayed by the state of the Middle East peace process which ground to a halt last year.
Mogherini has been criticised in Israel but she says EU policy of a two-state solution is the only way forward and has condemned Israeli settlement building in the occupied territories as a threat to the peace process.
Mogherini also announced Monday the nomination of Peter Burian, a senior official in the Slovak foreign ministry, as EU special representative for Central Asia.
The EU has over time appointed several special representatives, each tasked with a specific mission to help resolve major international issues of the day.