Jammeh chose exile in Equatorial Guinea, which is not party to the International Criminal Court, and left The Gambia.
Barrow won a December election, but for weeks incumbent Yahya Jammeh refused to recognise the result, setting off a crisis that saw the new president take his oath of office in neighbouring Senegal last week.
Worried for his safety, Barrow has yet to return from Senegal.
Speaking at a briefing in Nigeria's capital of Abuja Marcel Alain de Souza, head of the 15-nation Economic Community of West African States (ECOWAS), said the troops were working to secure Banjul and the surrounding area.
"Today or tomorrow, we will be able to indicate that President Adama Barrow, if he's comfortable, can fly on," De Souza said.
ECOWAS forces are investigating claims that armed mercenaries and weapons had seeped into the tiny West African nation during the weeks of turmoil when Jammeh refused to step down.
"It was said that a lot of arms were imported into the country. There were heavy arms and there were mercenaries who spoke neither English nor (the local language) Wolof. That an entire hospital was evacuated and filled with weapons and people who were armed to the teeth," De Souza said.
"President Adama Barrow has asked us two, three weeks so that we can evaluate whether there are stock piles of arms anywhere. Are there mercenaries hidden anywhere," he said.
"The forces need to go in to secure the environment. Imagine President Adama Barrow goes in, he wanted to go in since Sunday, what if he goes in and he is assassinated, the entire process will be put to question."
Barrow has requested the troops to stay in the West African country for "six months", said De Souza, adding that the decision to stay or leave is ultimately up to the ECOWAS defence chiefs.
Jammeh initially conceded defeat after the December 1 election, but the mercurial strongman then announced he no longer recognised the result.
Under the threat of a regional military intervention, Jammeh chose exile in Equatorial Guinea, which is not party to the International Criminal Court, and left The Gambia.
Barrow has assured Jammeh he will have all the rights legally ensured to an ex-president, which under Gambian law includes immunity from prosecution, barring a vote by two-thirds of the national assembly.