The option now under discussion is EPP candidate Manfred Weber to take the position of President of the European Parliament and Timmermans to lead the European Commission.
The diplomat said: "The combination of Timmermans for Commission and Weber for the European Parliament muster a majority in Parliament".
In 2014, the Spitzenkandidaten principle reinvigorated the influence of European political parties and of the European Parliament through the choice of lead candidates who would be subjected to a vote in the Parliament. The bloc also disagrees about the rules of picking a leader.
A first compromise around the Franco-German couple at the G20 summit in Osaka allowed for uniting the Dutch Prime Minister Mark Rutte, Emmanuel Macron, Angela Merkel and the Spanish Prime Minister Pedro Sánchez behind Frans Timmermans.
European Union rules demand that the top appointments achieve a balance of geographical spread, big and small countries and gender.
As some reporters slumped asleep over their desks, a high-ranking diplomat involved in the deliberations - a night-long series of bilateral talks, group gatherings and meetings, including over breakfast - said that former Dutch foreign minister Frans Timmermans was favorite to become the next European Commission president. And the liberals, led by French President Emmanuel Macron, have insisted the Spitzenkandidat system is not binding.
PAP has learnt from an unofficial diplomatic source that European Council President Donald Tusk has forwarded to the leaders of the European Parliament the propositions of France, the Netherlands, Germany and Spain, that the top EC position should go to the socialists, the head of the European Parliament to the Christian Democrats and the European Council to the liberals.
"This failure is that of division, political division in the EPP that marked the dissension of many of its leaders and geographic division within the council that led to deciding to reconvening tomorrow, and to find the necessary rest and for calm to return and a new solution that requires some to move a little".
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Ahead of the gathering, the Government said: "A candidate for President of the Commission. must be proposed by a qualified majority in the European Council and then elected by an absolute majority in the European Parliament".
Croatian Prime Minister Andrej Plenkovic, for his part, underscored that "everything is open" in the process of choosing candidates for the EU's top jobs.
There was hope at the previous summit on June 20-21 that more time would clarify who should replace Mr Juncker. If the European Council doesn't reach a compromise quickly, it risks losing its edge in the calendar of nominations - as the Parliament would have an even more considerable weight in the balance of negotiations.
The EPP and the S&D are the two biggest political groups in the European Union, but both lost seats in May's polls, where far-right and populist parties, pro-business liberals and the Greens made gains.
The summit will resume Tuesday.
But since no new name emerged from all-night negotiations headed by Donald Tusk, Timmermans remains the most likely victor, according to Reuters.
The longest ever EU summit has ended without agreement as Angela Merkel warned that with Brexit "looming" imposing the centre-left candidate Frans Timmermans as European commission president risked creating a risky split with the populist governments in Poland and Italy.
Another source said Vestager could serve as vice president of the commission.