The city was quiet overnight after hundreds of Gambians celebrated Barrow's swearing in and the subsequent ECOWAS advance into their country - a popular destination for European tourists that Jammeh has ruled with an iron fist.
Gambia's only land border is with Senegal and the regional coalition, which ECOWAS says involves 7,000 troops, has entered from the southeast, southwest and north.
Marcel de Souza, head of the ECOWAS commission, said Guinea's President Alpha Conde would travel to Banjul with the leaders of Mauritania and Liberia to try to convince Jammeh to travel to Guinea before choosing a country of exile.
"It's out of the question that he stays in place," de Souza said.
Jammeh initially conceded to Barrow after a December election before he reversed his decision, saying the vote was flawed and he would remain in power until a new election could be held.
Barrow has been recognised as Gambia's new president by world powers and Jammeh is increasingly isolated at home as ministers abandoned his camp.
On Thursday night, army chief General Ousman Badjie, who had publicly stood by Jammeh, was seen smiling on the streets, wading through a mass of jubilant Banjul residents shouting and dancing.
Barrow asked for foreign help to assume office immediately after he was sworn in on Thursday, a plan that was backed by the U.N. Security Council in New York.