The new offer would be complex, but in essence, would leave Siemens with control of Alstom's gas turbine business, the person with knowledge of the discussions said. The gas turbine business is considered one of Alstom's most attractive assets because of the boom in natural gas production in the United States and other countries.
Other units, such as those that supply equipment for distributing power around a network, would go to Mitsubishi, which might operate them as joint ventures with Alstom and allow the French government to retain influence.
Read MoreSiemens and Mitsubishi finalize Alstom offer
The offer would also preserve Alstom's brand name and identity, the person said, catering to French concerns about jobs and the company's status as a showcase of French engineering prowess. While some details of the offer were still in flux, there was no doubt that Siemens and Mitsubishi would formally submit a bid for Alstom.
Michel Sapin, the French finance minister, said on Sunday that an offer by Siemens and Mitsubishi, which said last week that they would join forces for a bid, would put pressure on G.E. "I think that G.E. will also sweeten its offer," Mr. Sapin said in remarks broadcast on iTélé and Europe 1 radio.
Both G.E. and Siemens have sought to convince the French government that they would create jobs in France and ensure that Alstom remains a symbol of French prowess. The French government does not own Alstom shares but has granted itself the power to veto any deals.
Read MoreGE's Alstom offer adds 1,000 French jobs: Sources
G.E. indicated on Sunday that it intended to continue pursuing Alstom. Completing a deal would help the American company expand abroad more quickly.
"G.E.'s alliance with Alstom creates jobs and global energy and transport champions in France," the company said in a statement on Sunday. "We have made progress in our discussions with the French government, including expanded alliances in the energy businesses with French investors as well as a global partnership with Alstom on transport. Alstom will remain a vibrant player in the energy and transportation industries."
The Siemens supervisory board includes representatives of shareholders as well as workers, and it must approve major decisions. The board met late Sunday to consider an Alstom bid but was not expected to issue a statement on its decision until Monday.
Read MoreAlstom shares rocket as it denies GE takeover talk
Although French officials had been very vocal about their opposition to G.E.'s bid for weeks, a solo bid by Siemens was also considered to be problematic in concentrating power with one company. Teaming up with Mitsubishi would answer antitrust concerns about combining the companies, and be more financially attractive to Alstom shareholders, a person with knowledge of the discussions said on Sunday.
In a second step later on, Siemens would give its rail business, which makes high-speed trains, to Alstom, which makes France's TGV high-speed trains. Siemens might be glad to unload the rail business, which has experienced problems in recent years, including delays in delivering the latest generation of high-speed trains to the German railroad.
Analysts have generally considered G.E. to be a more logical partner for Alstom because there is less duplication among businesses that supply turbines, transformers and other equipment to generate and distribute electricity. Alstom was seen as helping G.E. gain better access to fast growing markets in Asia, while G.E. would strengthen Alstom financially and prevent it from being eclipsed by larger rivals.
Read MoreGE industrial profits rise 12 percent, shares up
But Siemens, which has competed with G.E. since the 19th century, could not let Alstom go to its archrival without a fight. And the French government, its popularity slumping amid slow growth and high unemployment, has judged it can ill afford to have a French national champion fall into foreign hands. The government financed a bailout of Alstom in 2005.
Alstom's energy business, which last year contributed about two-thirds of the company's 20.3 billion euros of revenue, has well-regarded technology. But it has experienced slow growth in its home European market as well as a slump in orders for equipment for nuclear power plants.
Alstom's profit has been falling and there has been concern both in the company and in the government about whether the company will survive in an era where competitors have much greater scale and geographic reach, as well as the resources to finance big projects for customers.
Read MoreFrench warn GE as Siemens plans Alstom hijack
G.E.'s offer has the backing of Patrick Kron, Alstom's chairman and chief executive, and Martin Bouygues, whose family engineering and construction company is Alstom's largest shareholder, with about 29 percent. But the government solicited a bid from Siemens in hopes of keeping ownership of Alstom in Europe or at least putting pressure on G.E. to make assurances about jobs and the location of key facilities.
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