Alstom's board has accepted an offer from GE for the company's energy assets, Dow Jones reported, citing a source.
A preliminary deal worth at least $12 billion could be announced as soon as Wednesday, Dow Jones said.
Earlier Tuesday, Germany's Siemens said it would make an offer to the French engineering group if it is given four weeks to examine its books and draw up a detailed plan to rival the move by General Electric.
The interest in Alstom from U.S. competitor GE has triggered a fierce national debate about the fate of power turbine and train manufacturing in France - both integral to the nation's engineering pedigree.
Siemens said it had sent a letter to Alstom in the afternoon after its managing and supervisory boards had decided to make an offer.
"The prerequisite for this offer is that Alstom agrees to give Siemens access to the company's data room and permission to interview the management during a period of four weeks, to enable Siemens to carry out a suitable due diligence," it said.
It gave no further details of its plans, but at the weekend Siemens approached Alstom with a proposal to exchange part of its train business plus cash for Alstom's power arm. In a short letter, it had outlined its proposal worth $14.5 billion.
A source close to the discussions said a board meeting at Alstom had started early on Tuesday evening.
Sources close to the talks had said earlier that the French firm was likely to give Siemens two to three weeks to draw up a detailed plan to buy its power business.
Sources say Alstom already has a $13 billion cash offer from GE for its power business, which generates 70 percent of sales.
France's Socialist government has declared that it must have a say in the outcome, as thousands of jobs are at stake and state-owned utility EDF and the national railways are major clients of Alstom.
"There aren't only financial interests at stake in this matter; there are also industrial, social and human interests," Economy Minister Arnaud Montebourg said after a meeting with unions. "The government does indeed intend to defend our country's interests."
Alstom CEO Patrick Kron presented GE's interest to Montebourg last week. The company's shares were suspended and are due to resume trading on Wednesday.
After the counter-proposal from Siemens emerged at the weekend, Montebourg and President Francois Hollande arranged meetings with the parties in Paris on Monday.
Just over a week before Siemens boss Joe Kaeser presents his future vision for the Munich-based conglomerate, investors in Siemens were skeptical about a potential deal.
"We would have preferred a less risky strategy of organic growth," said Tim Albrecht, fund manager at DWS Investment.
A fund manager who declined to be named said: "Until last week, Alstom was seen as dead, and its products were not thought to be competitive."
"A purchase would be a 180-degree turn. If Siemens does this, they need very good arguments to justify it strategically."
The German government has said an Alstom-Siemens tie-up could offer "great opportunities". Montebourg described it as creating "two European and global champions", but Paris has not ruled out a deal with GE.
Some investors may also be wary of a French-German deal, given problems with previous cross-border tie-ups, such as EADS and drugmaker Aventis, which were both plagued at times by battles for control.
A tie-up between Alstom, with a market capitalisation of $11.5 billion, and Siemens, worth $144 billion, could raise antitrust questions, say some analysts.
However, some analysts and investors said they see Siemens' move as primarily defensive.
Rob Virdee, analyst at Espirito Santo Investment Bank, said the offer looked like a move to stop GE's expansion in Europe.
The French government denied a media report of another option that would involve selling some of the state's holdings in power utility EDF to finance an operation that would include a recapitalisation of the company.
—Reuters with CNBC.com