CMA CGM's controlling Saade family chose the Qatari sovereign fund as a new investor, according to Wansquare, the French financial newsletter.
Based on published reports, the Marseilles-based carrier reached an agreement with Qatari, but is continuing parallel talks with the U.S. equity fund Colony Capital, Wansquare said.
Qatari Holdings would take a 49 percent stake in CMA CGM, the world's third-largest carrier, according to media reports.
Qatari Holdings is said to have received the green light from CMA CGM's creditor banks for its investment in the carrier, which has 16,500 employees, including 4,000 in France.
FSI, France's state-backed investment fund which was established to help financially troubled strategic sectors, is negotiating with Qatari Holdings and Colony Capital over jointly acquiring a stake in CMA CGM.
CMA CGM said, "Discussions are ongoing and could conclude soon," but no decision has yet been made on a potential investor.
"These discussions are under way even while the group has strongly recovered during the first half of 2010 and this positive trend continues month after month," the company said.
Since October, CMA CGM has been negotiating with its creditors over a restructuring of its debt, much of it taken on to buy up to 45 new container ships.
The carrier booked a first quarter operating profit of $270 million following a $1.4 billion loss in 2009.
Last week, CMA CGM denied reports it had offloaded some of its debt onto its NYSE-listed affiliate Global Ship Lease from which it charters 17 ships.