He said he planned a meeting with GE management and had already met Kron on Thursday.
Alstom employs 18,000 people in France, about 20 percent of its global workforce.
Trading in Alstom shares was suspended pending a statement from the company. The shares closed up 10.9 percent on Thursday after Bloomberg reported that GE was in talks about a $13 billion full takeover bid for Alstom.
Read MoreAlstom shares rocket as it denies GE takeover talk
GE, with a market capitalisation of $265 billion, is about 23 times bigger than Alstom, valued at around $11.5 billion.
A deal to sell a power division beset by weak demand, low margins and industry oversupply to GE calls into question Alstom's existing plans to sell non-core assets and a stake in its transport arm to fill a hole in its balance sheet.
Kron told union representatives on Friday that there was no guarantee a deal would go through but he hoped to have answers for them "in the coming days", union sources said.
The head of Alstom's transport arm told Reuters in February the group was looking to list the unit separately as early as June if a trade buyer couldn't be found any sooner. De facto, if a deal with GE left Alstom with just its transport arm, a listing would no longer be needed.
"We will see what tomorrow brings," Kron reportedly told unionists. "I have to ensure a future for each of the group's units."
Alstom was bailed out by the French state in 2004 and relies heavily on orders from national rail operator SNCF and utility EDF. The group announced 1,300 job cuts last year and put assets up for sale to raise cash, including a stake in its transport business, which makes France's prized high-speed TGV trains. It also floated the possibility of an IPO of the business.
Ten years ago, when France was negotiating a bailout package for Alstom with European Competition Commissioner Mario Monti, German group Siemens was in the frame as a potential buyer of its power arm. In the end, the then French president, Nicolas Sarkozy, balked at that prospect of German ownership, and Alstom stayed intact.
Read MoreNokia seals Microsoft deal amid new CEO speculation
A report Friday's Le Figaro newspaper said Alstom has looked at a similar potential asset swap with Siemens more recently, whereby Alstom would have exchanged its power business against Siemens' rail business. Siemens declined to comment.
Before the takeover bid report, Alstom shares had slumped 20 percent in 12 months on concerns over its cash flow. Those concerns prompted Bouygues to take a $1.9 billion writedown on its Alstom stake in February. For GE, a deal could help the U.S. group get infrastructure assets cheaply and make cost savings in power generation. For instance, GE is looking to expand in smart grid technology, where Alstom is a strong player.
"We believe the recent reports that GE may only be interested in Alstom's power and grid businesses may reflect GE's goal to minimize challenges by the French government," William Blair analyst Nick Heymann said in a research note.
"The 'black box' related to this potential transaction remains the French government and GE's ability to secure the ability to restructure any nominally profitable Alstom assets it might acquire."