"I think I should quit now," Barrow told AFP. "He has lost the election, we do not want to waste time, we want this country to start moving."
Jammeh's party announced a legal challenge on Saturday during the Dec. 1 election in which it had already conceded defeat to Barrow.
Barrow must welcome a large delegation of African heads of state and UN representatives on Tuesday to persuade Jammeh to leave, which the president-elect said gave him confidence that he would soon take power.
"It is giving us confidence and giving every Gambian confidence that the world is worried about the Gambia," he said.
Diplomatic sources told AFP that the delegation is likely to include UN envoy for West Africa, Mohamed Ibn Chambas, Nigerian President Muhammadu Buhari and Liberian leader Ellen Johnson Sirleaf as head of the West African bloc ECOWAS.
Jammeh has directed the small piece of a nation of just under two million people for 22 years since taking power in a coup.
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