This could involve French state bank BPI acquiring a stake in Alstom alongside Mitsubishi, the Wall Street Journal reported on Sunday. But a source familiar with the situation said BPI was "ready to be involved in any scenario", including with Mitsubishi or GE.
A Bouygues spokesman said the group had not been approached by any party regarding a sale of its stake in Alstom, adding: "Bouygues wishes to remain a long-term shareholder in Alstom with a 29.3 percent stake."
Bouygues would support the proposal recommended by the Alstom board, he said.
In a second step, separate to a turbines deal, Siemens is also proposing to combine its rail activities with Alstom's, sources said.
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An Alstom spokeswoman declined to comment.
Finance Minister Sapin said he did not have "any preference" for a bidder, but France would defend jobs and investment through a new decree extending the government's powers to block foreign takeovers in sectors deemed strategic.
Alstom is a big private-sector employer in the country and was bailed out by the state a decade ago.
"We will not decide for (Alstom) but we will use our weight," Sapin said.
French President Francois Hollande will host a meeting on Alstom on Tuesday morning, according to his official diary, while Siemens Chief Executive Joe Kaeser is due to appear before a French parliamentary committee later that day.
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Montebourg reiterated in a newspaper interview on Friday that he favored an alliance that preserved Alstom's identity, industrial sites, decision centers and jobs.
He said a tie-up with Mitsubishi would be "a serious alternative" to GE's proposal.