Kron however said no decision on a deal would be made at a board meeting to be held in the afternoon, one of the sources said.
"I don't validate the rumours out in the American media of a takeover offer from General Electric," one of the sources cited Kron as telling a European works council meeting.
"What is exact, is that we are in talks over an industrial deal."
Kron did not give further details on the discussions, both sources said.
Economy Minister Arnaud Montebourg told Le Monde newspaper that the government was working on "other solutions and scenarios" for Alstom, but did not go into more detail.
France's government weighed into the furore over the future of the country's struggling engineering group Alstom on Friday and the stock market regulator forced a suspension of trading in its shares pending a company statement.
"The government expresses patriotic concern and watchfulness with regard to Alstom," he said. "This concern is focused on the serious risk of losing a major decision centre."
"With the prime minister (Manuel Valls), we will meet the president of General Electric in order to focus our talks on these concerns," he said, adding that he had met Alstom's chief executive on Thursday.
Speaking a day after Bloomberg reported GE was discussing a takeover with the transport and power group, a source close to the matter told Reuters Alstom would hold a board meeting on Friday afternoon.
Alstom declined to comment.
Shares of Alstom closed up 10.9 percent on Thursday after the Bloomberg report said it was in talks to buy it for about $13 billion.