The village, divided between Lebanon and the Golan Heights which were annexed by Israel in 1981, is the last position occupied by Israeli forces since their October 1 pullout during its recent offensive in the country.
A statement from the United Nations Interim Force in Lebanon (Unifil) said the deputy Unifil commander had met senior Lebanese and Israeli officers to discuss the withdrawal.
"The situation around Ghajar was discussed with a view to ensuring a speedy withdrawal of IDF [Israel Defence Forces] from the area," Brigadier General Jai Prakash Nehra said.
"The meeting was productive and the main focus was to finalise arrangements for Ghajar after the IDF withdrawal."
It said that "minor administrative issues" regarding the town's residents were "still pending" but that Unifil hoped they could be resolved by next week.
One third of the village is in Lebanese territory and two-thirds in the zone annexed by Israel.
Ghajar is dissected by the "Blue Line" designating the Lebanon-Israel border that was drawn by the UN in 2000.
It was occupied by the Israeli military during its 34-day offensive in July and August against fighters from Hezbollah, the Lebanese Shia militia, following the kidnap of two Israeli soldiers by its fighters.
The withdrawal of Israeli forces from Ghajar, and also from the disputed Shebaa Farms where the Lebanese, Syrian and Israeli borders meet, is one of the demands of the government in Beirut.