Turkey's NTV news channel said the meeting took place in a hotel suite in Brussels, where the Turkish minister was on a visit to discuss his country's bid to join the European Union, and lasted more than two hours.
The two discussed ways of repairing bilateral ties, with Davutoglu insisting Israel must apologise over the deadly raid on the Turkish ferry Mavi Marmara, the channel said, without citing a source.
The meeting was kept secret also from Turkey's chief EU negotiator Egemen Bagis and Agriculture Minister Mehdi Eker, who were in Brussels with the foreign minister, the report said.
Davutoglu and Ben Eliezer agreed to keep the meeting secret, share their discussions with their prime ministers and meet again secretly on a future date, it added.
Aides to Davutoglu and Prime Minister Recep Tayyip Erdogan contacted by AFP declined to either confirm or deny the meeting.
If confirmed, it would be the first between the sides at ministerial level since a deadly May 31 Israeli commando raid on a Turkish ship leading an aid flotilla to Gaza in defiance of an Israeli blockade.
The incident, in which troops killed eight Turks and a dual US-Turkish citizen, shattered Turkey's already strained ties with Israel. Ankara recalled its ambassador and cancelled three planned joint military exercises.
The two countries had been close allies until their friendship soured amid sharp Turkish criticism of Israel's December 2008-January 2009 war on Gaza.
Relations were strained further when Israeli Deputy Foreign Minister Danny Ayalon gave Turkey's ambassador a public dressing down to protest against a Turkish television series which showed Israel in a bad light.
But the talks between Ben Eliezer and Davutoglu were concealed from the Israeli foreign ministry, infuriating the hawkish and outspoken minister, Avigdor Lieberman, Channel Two said.
While not mentioning Ben Eliezer or Davutoglu by name, Lieberman's office said talks had taken place without its knowledge or approval.
"The foreign minister takes a very serious view of the fact that this occurred without informing the foreign ministry," it said in a statement.
"This is an insult to the norms of accepted behaviour and a heavy blow to the confidence between the foreign minister and the prime minister."
A statement from Prime Minister Benjamin Netanyahu's office said he had approved a request from Ben Eliezer to hold an unofficial meeting with a "Turkish personality" and the failure to coordinate with the foreign ministry had been due to "technical reasons".