The OAS chief had flown to Honduras on Friday to demand that the interim government restore Zelaya.
The 35-member OAS has set a Saturday deadline for the military-backed interim government to comply with its demands.
It has threatened to expel Honduras from the regional grouping if it fails to meet its deadline.
Cristina Fernandez, the Argentine president, will accompany Zelaya from Washington DC, the US capital, to Honduras on Sunday, an Argentine government source said on Friday.
"Tonight she's traveling to Washington. On Sunday, she'll leave from Washington to Honduras," the source told reporters, on condition of anonymity.
Rafael Correa, Ecuador's president, and Miguel D'Escoto, the president of the UN General Assembly, will also accompany Zelaya, the source said.
Lucia Newman, Al Jazeera's Latin America editor, said that several scenarios to solve the crisis had been proposed by OAS member states.
"One of them is that this de facto government, as the OAS calls it, would issue a blanket amnesty that would annul the arrest order for Zelaya," she reported from Tegucigalpa.
"In exchange, elections [currently scheduled for January] would be brought forward. But the deposed president would have to be reinstated [pending the election's outcome]. I understand that this proposal was put forward by Argentina."
However, the military-backed interim government and Roberto Micheletti, the interim president, have said that while they will consider bringing forward the elections, they are not willing to reinstate Zelaya for any length of time.
A large demonstration in support of the interim government went ahead in Tegucigalpa as Insulza arrived in Honduras.
|Zelaya is set to return to Honduras accompanied by regional presidents [EPA]
But supporters of Zelaya trying to enter the capital said they were prevented from joining a large demonstration in the city calling for the deposed president to be reinstated.
"The pro-Micheletti demonstration is huge. Pro-coup supporters have been bussed in from all over the country, we understand," Newman reported.
"But on the other hand, those [pro-Zelaya supporters] who wanted to demonstrate in front of the head of the OAS have been kept away; their buses have not been allowed to enter the capital."
Insulza has already said he will not talk to members of the military-backed interim government since his organisation does not recognise it.
Newman said that the current crisis is the "biggest challenge that the OAS has ever had to face".
"There is absolute consensus in the international community that they have to use their diplomatic might to reverse this coup d'etat. There is consensus that this kind of thing can not happen, and should not happen," she said.