The stake in Oil Mining Lease (OML) 118, which is located some 120 kilometres (75 miles) off the Niger Delta, is valued at up to $750 million, according to two of the sources.
Investment bank Rothschild is running the sale process for Total, the sources said.
A spokeswoman for Total declined to comment. Rothschild declined to comment.
OML 118 is operated by Royal Dutch Shell, which holds a 55% interest. Exxon Mobil holds a 20% stake in the block, while Italys Eni and Total each hold 12.5%.
The sale process is part of Totals plan to sell $5 billion of assets around the world by 2020, the sources said.
The block includes the Bonga field, Nigerias first deepwater project which started in 2005 and produced around 225,000 barrels of oil and 150 million standard cubic feet of gas per day at its peak.
Output from the block is planned to grow sharply with the $10 billion development of the Bonga Southwest field which is expected to produce up to 200,000 bpd, roughly 10% of Nigerias current oil production.
Nigerias vast oil resources have attracted foreign oil companies for decades but changes to the countrys oil revenue laws as well as an unexpected tax levy over the past year could make investments in offshore projects less attractive.
Shell and its partners were expected to make an investment decision on Bonga Southwest last year but uncertainty over its fiscal terms with the Nigerian government have delayed the process.
Shell in February launched a tender for bids for a 225,000 bpd floating production, storage and offloading vessel for the new development phase. It has since pushed back the schedule for the bids.
The sale comes as Total prepares to expand its operations in Africa after agreeing earlier this year to buy Anadarkos Africa portfolio for $8.8 billion as part of its acquisition by U.S. rival Occidental Corp.
Total in January started production from the Egina oilfield off Nigerias coast which is expected to plateau at 200,000 bpd of oil.
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