There are reports, which have not been confirmed by Siemens, that the German group has offered to buy Alstom's energy business and give the French giant part of its train activities in return.
Meanwhile in Berlin, a spokesman for Germany's economy ministry said a possible tie-up between Alstom and Siemens would offer "a big opportunity and great potential in terms of industrial policy for Germany and France."
Earlier on Monday, French President Francois Hollande had an hour-long meeting with Jeffrey Immelt, the boss of US giant General Electric. Hollande is keen to stop one of France’s most important companies falling into the hands of the American GEC.
The French president pressed his case for jobs and Alstom's decision-making centre to remain in France.
"There were legitimate issues [raised by the government] which GE is working on," said a GE source. "There is still work to be done and that's normal. GE is on the case," the source added.
Immelt nevertheless described his talks with Hollande as an "open, friendly and productive".
Hollande is also having talks with Martin Bouygues, the head of Bouygues, the French construction telecom and media company, which is a key shareholder in Alstom.
The flurry of talks is part of a race by the French Socialist government to keep Alstom's decision-making centre in France and protect jobs and strategic energy interests, in what Economy Minister Arnaud Montebourg has described as a "patriotic" response to an expected bid by GE.
At the end of last week it emerged that GE was in advanced talks to buy Alstom's energy interests for about 10 billion euros.
Energy activities account for about 70 percent of Alstom's business, with the rest being focused mainly on making railway equipment including the TGV high-speed train.
GE already has major energy manufacturing activities in France, but Montebourg objected on Monday to the possibility that Alstom "in three days, can decide to sell 75 percent of a national jewel behind the backs of the employees, of the government, of most of the board and of the senior executives."
He told RTL radio that a bid from GE raised a simple problem that "the main part of Alstom, 75 percent of the businesses, 65,000 employees in the world, is going to be run from Connecticut."
Alstom is under pressure because its main markets for power generation and rail equipment are expected to be weak in the next few years.
Its share price has fallen heavily in the last year, pushing Bouygues into loss, although Alstom shares jumped on the bid reports.
Economists say that Alstom is too small alongside giants such as GE and Siemens and that it is uncompetitive.
They also comment that the French government, since selling its stake in 2006, has little real control over what the Alstom board decides.
Ten years ago, when Alstom had to be rescued and was divested of its shipbuilding interests, France rebuffed takeover interest from Siemens.
The case of Alstom is highly sensitive politically and is also seen as emblematic of deep strains in many parts of French industry.