Such a deal could give GE control of Alstom's high-speed TGV trains and rail-signal technology, according to the reports, but the French firm has said that it has not been informed of any potential public offer on its shares.
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French newspaper Le Figaro has reported that the discussions will solely focus on Alstom's energy arm including gas turbines, coal,distribution and offshore wind business -- omitting the group's TGV train manufacturing business.
In a press release on Thursday morning, Alstom said it constantly reviewed the strategic options of its businesses and plans to communicate its annual results on May 7, as scheduled.
Ishaq Siddiqi, a market strategist at London-based spread better ETX Capital said that traders weren't totally convinced with the announcement from Alstom which has led to Thursday's rally in its stock price.
"(It) hasn't exactly flat-out denied it, which will keep the bid chatter propping up the French company's shares today." he said in a research note.
Successive French governments have a long history of blocking foreign takeovers of key domestic companies, claiming that they are off vital strategic importance to the country. Last year, Paris refused to give the go-ahead to Yahoo's takeover of the French video-sharing site Dailymotion, while back in 2005 a potential 30 billion euro bid by Pepsico for food and dairy giant Danone was also halted.
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Bernard Charles, chief executive of design software company Dassault Systemes, told CNBC that he could see no reason for the government to block a bid for Alstom if one was made.
"I think the government would be smart enough to think about the long-term interests of this industry and I think that, despite the political statement, the economic decisions will be smart," he said.
"I don't think there is any reason to block something that could be of best interest for the industry and for the development of this company."