Executives from Siemens and Mitsubishi Heavy Industries have met French President Francois Hollande for talks about buying parts of engineer Alstom.
The companies are bidding against US firm General Electric, which also wants to acquire the French company's assets.
However, there are reports that advisers to Mr Hollande told the bidders to raise the terms of their offer.
Talks with all the parties are expected to continue over the next few says.
Siemens would pay 3.9bn euros (£3.1bn) for the gas turbine arm, while Mitsubishi would buy 10% of Alstom and inject 3.1bn euros into the company.
General Electric has offered $16.9bn (£10bn) for Alstom's energy business.
Siemens also plans to discuss the possibility of creating a combined rail business with Alstom, which makes the high-speed TGV trains.
There are fears in France that the bid battle will end with the break-up of Alstom and the loss of jobs.
All the bidders have pledged job creation and investment, but Reuters news agency reported that during the meeting with Mr Hollande, the Siemens-Mitsubishi delegation was told that the "terms must be improved".
The French government can block foreign takeover bids for companies deemed "strategic" and has made job preservation a priority at Alstom. The company is one of France's key industrial firms.
Alstom had to be bailed out by the French government in 2004. It has suffered heavy debts and a fall in orders over the past 10 years
(BBC)