The officials, whose names were not reported, described the expanded aid as around $100 million in non-lethal military gear such as night-vision goggles and body armor.
Kerry has told U.S. lawmakers the equipment will give the rebel fighters a boost on the battlefield and may help convince Syrian President Bashar Assad the tide is turning against him.
Kerry was in Istanbul to confer with member nations of the Friends of Syria group. He had a separate meeting scheduled with Palestinian President Mahmoud Abbas, Turkey's Today's Zaman said.
The new U.S. aid proposal for Syria comes as the European Union is moving closer to lifting its arms embargo on Syria, which could result in more firepower for the rebels, CNN said.
The Obama administration remained leery about shipping weapons into Syria for fear they could wind up in the hands of a growing number of militant Islamic jihadists infiltrating Syria, the report said.
Supporters of arms shipments say it would be better to bolster the more-moderate factions of the rebels so they can take over when and if Assad's government falls.
"Everybody has now accepted a concern about extremist elements who have forced their way into this picture, and there is a desire by all parties to move those extremist elements to the side and to give support, I believe, to the (moderate) Syrian opposition," Kerry said Thursday.