The offer came on the heels of reports that the US giant wants to buy the French engineering group, which manufactures the country's groundbreaking high-speed TGV trains.
Alstom is a politically-sensitive symbol of engineering prowess in France and a key exporter, seen as one of the jewels of French industry.
GE chief Jeff Immelt was expected in Paris today but a meeting with France's Economy Minister Arnaud Montebourg was deferred by his office, which said the minister needed more time to examine the offers following Siemens' announcement.
Earlier press reports said GE's boss could also meet with Prime Minister Manuel Valls today. But informed sources in the government said no such meeting had been pencilled in as yet.
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Montebourg, a fierce protector of French industry, has pledged to study various options for Alstom following reports that GE would bid to buy the company's power-generation division, accounting for more than 70 per cent of its business with revenues of USD 19 billion.
He has said the government was exercising "patriotic concern and vigilance" while handling the case.
Although the French state has not held a stake in Alstom since 2006, France's Socialist government wants to obtain guarantees on "jobs, the location of activities and energy independence", according to President Francois Hollande's office.
US giant GE has 305,000 employees around the world and its revenues last year were USD 146 billion.
Press reports have said GE was ready to fork out 10 billion euros for Alstom's energy division, the largest part of its businesses but which does not include the unit that makes high-speed trains.