Both sources said GE was not in exclusive talks with Alstom, which is set to also receive an offer from Germany's Siemens. One source said GE had offered to pay about 10 billion euros for the unit.
"Alstom's board has accepted the GE offer, it will be examined by an independent committee," one source close to the talks told Reuters.
"The two groups will not enter into exclusive negotiations. This means Alstom cannot go and look for other offers, but there is nothing to stop it from examining offers it receives without soliciting them," the source added.
Earlier on Tuesday, Germany's Siemens <SIEGn.DE> said it would make an offer to Alstom if given four weeks to examine its books and draw up a detailed plan to rival a move by GE.
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," Siemens 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.
(By Matthieu Protard and Maria Sheahan; Additional reporting by Arno Schuetze and Sabine Wollrab in Frankfurt, Irene Preisinger in Munich, Benjamin Mallet, Mark John, Geert De Clercq and Gregory Blachier in Paris, Lewis Krauskopf in New York, and Sophie Sassard in London; Writing by Andrew Callus, Mark John, Madeline Chambers and Geert De Clercq; editing by Will Waterman and David Gregorio)