Mr Barrow is quoted by AFP news agency as saying:
It's giving us confidence and it will give confidence to every Gambian that the world is concerned about Gambia."
Mr Barrow won the election by a narrow margin
AFP reports that apart from Nigeria's President Muhammadu Buhari, the delegation is likely to include Liberia's President Ellen Johnson-Sirleaf in her capacity as head of the West African regional bloc Ecowas and UN West Africa envoy Mohamed Ibn Chambas.
Ghana's President John Mahama is also expected to attend.
Mr Mahama has accepted his defeat in Ghana's election, and has promised a smooth transfer of power to incoming President Nana Akufo-Addo.
Mr Barrow rejected Mr Jammeh's decision to challenge the result in the Supreme Court, saying:
We don't have time to fight again. The Supreme Court wasn't existing for the last one year. There are a pile of cases that are waiting... but he doesn't care about it."