Immelt also indicated that GE is considering giving Alstom control of GE's signalling business to strengthen Alstom's remaining transport division.
After the talks, one of President Hollande's officials acknowledged that GE's detailed offer had been improved and strengthened, but also said that more work on the offer is still needed.
Until now the French government has been hostile to GE's attempt to acquire Alstom's power division and has favoured a potential offer by Siemens which would involve Siemens taking over Alstom's power division in return for Siemens merging its railway business with that of Alstom's.
Siemens is expected to make an offer by June 16, while GE has extended its offer until June 23. However, Siemens is in the midst of another major reorganisation and its railway activities are split across several divisions which would complicate a merger with Alstom. A merger of the Siemens and Alstom rail businesses is also likely to be scrutinised by European competition authorities.