On Tuesday, Libya's armed forces posted a Facebook photo of Hifter, a powerful general who lived for years in the US, and Fayez, the prime minister of the United Nations-backed government in Tripoli.
The UAE is, with Egypt, the main supporter of Field Marshal Khalifa Haftar, whose forces control most of eastern Libya, including its key oil ports, and who refuses to recognise the UN-backed government of Fayez al-Sarraj.
Haftar will be nominated for president of Libya in March 2018 in an agreed on upcoming elections for president and for the parliament, the sources revealed, adding that Al-Serraj expressed satisfaction with this point.
The UAE on Wednesday hailed a meeting in Abu Dhabi between two rival Libyan leaders as a significant breakthrough in talks aimed at ending the conflict. The two met Tuesday in the UAE capital for what the Libyan military described as "Arab and worldwide mediation" over that country's long political crisis.
The two men met face-to-face in Abu Dhabi on Tuesday, the LANA news agency said, for only the second time since Sarraj was named prime minister-designate after a UN-backed deal in late 2015.
Emirati officials did not immediately comment on the meeting.
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That passage appeared to be a subtle dig at Qatar and Turkey, which had supported Islamists in the country.
The United Arab Emirates voiced optimism a political settlement could be reached in Libya after the meeting.
Egypt and the UAE have been spearheading regional efforts to mediate between rival authorities in eastern and western Libya as fighting has threatened to plunge the country into all-out war.
"The UAE believes that any solution that brings stability to Libya should come from and be supported by the Libyans and should be purely based on Libyan-Libyan dialogue", the Foreign Ministry said. It's unclear if talks on Libya will continue during his visit and if he'll be involved.
Libya has remained in a state of turmoil since early 2011, when leader Muammar Gaddafi was ousted and killed in a bloody uprising - backed by North Atlantic Treaty Organisation airpower - after 42 years in power.
It stressed the need for "upholding the goals of the February revolution" against Gaddafi, building up an army under civilian control, combating terrorism, defusing an escalation of violence in the south and "taking all measures that guarantee the peaceful hand-over of power".