And in that nightmarish scenario for Turkey, it would be left completely at the mercy of Haftar and his allies - UAE and Egypt - and they'll make sure that after having Greece on board, Ankara doesn't get a slice of the Mediterranean pie.
On Monday evening, Haftar asked for more time to look over the agreement already signed by Fayez al-Sarraj, the head of the UN-recognised government.
Turkish President Tayyip Erdogan and US President Donald Trump discussed developments in Libya in a phone call on Wednesday, the White House and Turkey's presidency said, ahead of the Berlin summit.
On Thursday, German Foreign Minister Heiko Maas' office said that Haftar committed to a ceasefire and was willing to attend the Sunday conference, after Maas visited the commander in his base in the eastern Libyan city of Benghazi.
It is hoped both the UN-backed government and forces loyal to Russian ally Gen Khalifar Haftar will sign a ceasefire.
Both sides in Libya's conflict are expected Monday in Moscow to sign an agreement on the terms of a ceasefire which went into effect over the weekend, ending nine months of fighting after weeks of global diplomacy.
Turkey and Russian Federation failed to convince Haftar on Monday to sign a binding truce to halt his nine-month campaign to try to conquer the Libyan capital, Tripoli.
Since the 2011 ouster and killing of Libya's longtime dictator Moammar Gadhafi, the country has sunk further into chaos and turmoil.
He also warned against "external interference", which he said would "deepen the ongoing conflict and further complicate efforts to reach a clear global commitment to a peaceful resolution of the underlying crisis".
Haftar's offensive against Tripoli upended United Nations efforts to broker a political settlement.
"In order for the legitimate government in Libya to remain standing and for stability to be established, we are now sending our soldiers to this country", Erdogan told an event in Ankara.
Officials from Russia, Turkey, France, China, the United Arab Emirates and the United Kingdom - as well as several African and Arab countries - are also invited.
Turkey backs Haftar's rival, Serraj, while Russian military contractors have been deployed alongside Haftar's LNA forces. Turkey and Russia's diplomatic initiative came despite the countries being seen as supporting opposing sides.
"We will begin search and drilling activities as soon as possible in 2020 after issuing licenses for the areas", Erdogan said during a two-hour speech in the capital, Ankara.