Several sources close to talks between the companies said on Friday a transaction could be announced in days. Some put a $13 billion valuation on Alstom's turbines and power grid equipment business.
Sources close to the government who flagged the likely meeting between economy minister Arnaud Montebourg and Immelt said Prime Minister Manuel Valls might also meet the chief executive, who heads one of the 10 largest investor-controlled companies in the world, should the more senior politician return from a visit to Rome in time.
French media said a decisive Alstom board meeting, the second since Friday, would also take place on Sunday.
Socialist Montebourg has been a strong exponent of France's traditionally cautious approach to foreign takeovers of companies in flagship industries.
Last week he said he would protect the national interest and study "other solutions and scenarios" for Alstom, also the maker of TGV high-speed trains and one of France's top private-sector employers, which is struggling with heavy debt and weak demand.
However, one source close to the talks said the government had been looking for alternatives for months without success "so I don't see what they will find now".
Nevertheless, political sensitivities run deep.
"I ask you, prime minister, to please tell the shareholders and management of the groups concerned that this transfer of control is out of the question," former Socialist minister Jean-Pierre Chevenement said in an open letter to Valls published by Les Echos newspaper on Saturday.
Montebourg met Alstom chief executive Patrick Kron on Thursday and said on Friday he would meet "shortly" with Immelt.
An industry source close to the talks said GE would argue there was not much concern about job cuts in France, where Alstom employs 20 percent of its workforce, some 18,000 people. The source noted that in gas turbines, for example, GE has its own gas turbine making business in France while some of Alstom's is in Switzerland.
"The French state is asking for assurances from GE, all that is a game that implies a discussion around the disappearance of national champions," said the source. "Conversely, GE will try not to offer too much."
Sources have said a deal is backed by Alstom's main shareholder, French conglomerate Bouygues with 29 percent. Alstom's Kron told union officials on Friday he was discussing an "industrial operation" but did not name GE. Bouygues and GE have declined to comment.
A deal to sell Alstom's power assets, which account for about 70 percent of total group revenue, would effectively break up the engineering group and leave Alstom as a pure transport business building its well-known high-speed TGV trains, other rolling stock and transport industry equipment.
It could, however, be less politically sensitive than a full takeover offer for the company, talk of which caused Alstom shares to soar on Thursday.
Alstom was bailed out by the French state in 2004 and relies heavily on orders from national rail operator SNCF and utility EDF. It employs 93,000 worldwide, with about half of its French total of 18,000 in the power business.
Alstom's power assets include turbines for coal, gas and nuclear power plants, wind farms and systems for power transmission and distribution.
The trading of Alstom shares was suspended on Friday after a report GE planned a full takeover of the company. Before that Bloomberg report, Alstom shares had slumped 20 percent in 12 months on concerns over its cash flow, and its weakening prospects prompted Bouygues to take a $1.9 billion writedown on its stake in February.
Alstom is less than one-twentieth the size of GE and much smaller than its European archrival, German group Siemens AG , and its orders have slumped since the 2008 economic crisis depressed demand for power equipment.
In need of raising cash, Alstom reached out to GE, two industry sources said.
Industry sources said Alstom was strong in steam turbines used by the nuclear industry, while GE was a top player in gas turbines and not so strong in steam. A deal would also enable GE to expand into wind power and grid technology, they added.
The deal would let GE "materially strengthen its competitive position in the global power market," said Brian Langenberg, an analyst with Langenberg & Co.
GE, which already employs over 10,000 people in France, has said it wants to increase its earnings contribution from industrial operations relative to its financial activities.
Ten years ago, when France was negotiating a bailout for Alstom with European Competition Commissioner Mario Monti, Siemens was a potential buyer of its power arm. In the end, then French president Nicolas Sarkozy balked at the prospect of German ownership and Alstom remained intact.
French newspapers have reported a possible re-launch of attempts from that the time to engineer a swap of Alstom's power business with Siemens' rail business as an alternative to a GE deal. Siemens declined to comment.