The investment would include a gas processing plant and a pipeline, said the source who is privy to the agreement but could not be named as they were not authorised to speak on the issue.
Total declined to comment.
The NNPC source said an announcement would be made this week.
The gas processing facility will be built on the Ubeta onshore gas field, jointly owned by Total and NNPC, and will supply gas to the Nigeria Liquefied Natural Gas (NLNG) plant.
NLNG is a consortium between NNPC, Shell (SHEL.L), opens new tab, Total and Italy's Eni (ENI.MI), opens new tab.
When completed, the plant would generate 350 million standard cubic feet per day of gas and 10,000 barrels per day of associated liquids, said the source.
Nigeria, which holds Africa's largest natural gas reserves of more than 200 trillion cubic feet, flares - or burns off - gas from its oil fields because it lacks processing infrastructure and faces capital constraints.
The latest investment could mean President Bola Tinubu's bid to attract investment into Nigeria's energy sector is beginning to succeed, analysts said.
"The government will hope this offers confidence not only in the quality of the Nigerian resource base, but also in the government's pledge to improve ease of doing business," Clementine Wallop, director, sub-Saharan Africa at political risk consultancy Horizon Engage, said.
Energy analysts say Nigeria has failed to increase its exports to the European Union after the bloc sought alternative supplies to make up for lost Russian imports because of the Ukraine war. Locally, Nigeria is struggling to feed its gas power plants that generate most of its grid electricity.
