Some sources familiar with the talks cast doubt on whether Alstom would be interested in the new deal sketched out by Siemens. Still, a rival offer would give the French government more leverage with GE after it gave itself the power to block foreign takeovers in "strategic sectors".
The French government has repeatedly criticised GE's bid, favouring alliance between the companies rather than a straight sale of Alstom's power arm - which accounts for 70 percent of the group's revenue - that would leave the French group with just its smaller transport business.
Read MoreGE's Immelt: Alstom deal will increase earnings, bump upindustrial mix
Meanwhile it has advocated an alternative European tie-up between Alstom and Siemens. Initially though, it faced reluctance from both firms, long bitter rivals.
But after several trips to Paris by CEO Joe Kaeser and nearly two weeks of access to Alstom's data, Siemens has warmed to the idea and has been refining its bid to make it more attractive to Alstom and the French government, sources said.
"Siemens is presenting the following case: it will create national champions in trains and energy. Everything will be kept in Europe. It has offered some new elements, which sweeten its proposal," said a source familiar with the proposed deal.
In a short letter to Alstom late last month, Siemens had outlined a proposal worth $14.5 billion, offering to exchange part of its rail business plus cash in exchange for Alstom's power assets.
Two sources familiar with the talks said Siemens was now discussing handing over all of its rail business to Alstom and setting up a joint-venture in rail signalling.
Read MoreFrench warn GE as Siemens plans Alstom hijack
To limit the German firm's influence in the resulting transport-focused Alstom group, Siemens is also discussing with Paris and Berlin the opportunity for France - which owns 0.9 percent of Alstom's capital via state fund CDC - to take a more sizeable stake, political and financial sources said.
One source said the French government could take a stake of over 10 percent in Alstom, as it seeks to secure the domestic roots of the engineering group which received a state bailout a decade ago and is a big private employer in the country.
On Friday, French Economy Minister Arnaud Montebourg said the government would not let domestic companies be "dismembered, chopped up into pieces and devoured" and did not rule out taking a stake in Alstom to help secure its future.
Read MoreGE in talks to buy France's Alstom for $13 bln: Report
Meanwhile Siemens could offer to sell Alstom's wind and nuclear power assets to French state-controlled energy group Areva thereby addressing government concerns over France's energy independence, said two sources familiar with the proposed deal.
As a further sweetener, Siemens is said to be offering to set up in France the headquarters of sub-units in Transmission and Distribution - the segment which makes gear to carry electricity from power plants to households - potentially strengthening the country as a hub for this technology.
Siemens declined to comment. It has previously said it plans to use the full four weeks allotted to it for due diligence, and then decide on whether to make a formal offer.
Read MoreAlstom shares rocket as it denies GE takeover talk
Alstom declined to comment beyond saying it was reviewing GE's bid and had received an expression of interest from Siemens, but no formal offer.
General Electric and Areva also declined to comment. Representatives for French state fund CDC could not be reached outside European business hours.
Kaeser, vaulted into the top job at Siemens nine months ago after his predecessor Peter Loescher was ousted in a boardroom coup, unveiled a restructuring earlier this month that puts a premium on profitability over growth.
As a result, he has seemed lukewarm about a tie-up with Alstom, saying at a recent strategy presentation in Berlin that his firm would not be forced into a bid.
Read MoreGE industrial profits rise 12 percent, shares up
But the new French decree, which gives the government formal powers to overrule foreign takeovers in "strategic" sectors from energy, water and transport, to telecoms and health, underscored for Siemens the lengths Paris is willing to go to pave the way for a European-only deal.
"Let's just say that the landscape seems to have shifted to our advantage," one official close to Siemens told Reuters.
However, sources close to Alstom say it wants cash and backs GE's bid, and while it does want to expand in rail signalling it is not interested in taking on more rolling stock.
Other impediments to a Siemens deal include antitrust concerns and opposition from unions. A German-French deal would imply more industrial overlap, raising the risk of job cuts and forced asset sales - especially in trains.
After competing aggressively for decades, Siemens and Alstom would also have a deep cultural divide to overcome.
Alstom CEO Patrick Kron has been referred to as a "Siemens hater" in the German press. Kron has rebuffed the tag, but industry sources say he has never forgiven the German group for lobbying against a state bailout for Alstom a decade ago in the hope of buying some of its assets.
Overall, GE remains ahead in the race for Alstom's assets, said one source close to the talks: "We are not at the stage where we are negotiating with Siemens a contract that could be signed tomorrow."
Follow us on Twitter: @CNBCWorld