Nigeria’s president flew to Banjul to try to broker a deal but Mr Jammeh would not relinquish power.
Mr Barrow is now heading to Mali, where he will meet West African leaders attending a summit there.
The former estate agent wants to resolve the transitional deadlock so he can be sworn in next week.
President Jammeh’s term ends on Thursday.
The African Union has said it will no longer recognise Mr Jammeh’s rule beyond this point.
Nigerian leader Muhammadu Buhari had flown to The Gambia’s capital, Banjul, to try to broker a deal, as the region fears the consequences of a non-peaceful transition.
Ecowas, a 15-nation bloc of West African states that organised the delegation, has it said it would consider removing Mr Jammeh using military force if he refuses to step aside.
Mr Barrow is travelling to Mali with the Ecowas delegation for further discussions this weekend.
Mr Jammeh had initially admitted defeat after the December election. But shortly afterwards he called for the result to be annulled.
The 51-year-old leader seized power in the country in 1994 and has been accused of human rights abuses, although he has held regular elections.
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