The companies may announce the deal as early as next week, the report cited the people as saying. It said the deal would give GE control of Alstom's high-speed TGV trains and rail-signal technology and that the move had the support of Bouygues (BOUY.PA), Alstom's biggest shareholder with a 29 percent stake.
An Alstom spokeswoman denied the report, saying "these are totally unfounded rumors". A Bouygues spokesman was not immediately available to comment. A GE spokesman declined to comment.
Alstom has been hit hard by a drop in orders for power equipment from utilities, which are suffering in turn from weak electricity prices. The group announced 1,300 job cuts last year and put assets up for sale to raise cash, including a stake in its transport business, which makes France's prized high-speed TGV trains.
Alstom shares have slumped 20 percent in the past 12 months on concerns over its cash flow. The group now has a market capitalization of about $10.37 billion, according to Thomson Reuters data.
GE has been targeting acquisitions in the $1 billion to $4 billion range, but comments from executives on its first-quarter conference call last Thursday signaled to some analysts that the company would be willing to strike a larger deal.
Chief Financial Officer Jeff Bornstein said in an interview last Thursday that the conglomerate would consider spending more if the deal was "absolute strike zone," including targets that fit with its main businesses and offer significant cost savings.
GE Chief Executive Jeff Immelt is seeking to increase the company's profit contribution from its industrial manufacturing businesses, while reducing exposure to its GE Capital finance unit.
Reporting by Aman Shah in Bangalore, Natalie Huet in Paris and Lewis Krauskopf in New York; Editing by Savio D'Souza