The latest I know of is that Boeing will help GF lease some aircraft until they get new 787. There was talk of 777 however the start-up cost for running a fleet that will be temporary is too high - you have to remember GF is cash strapped.
So efforts are on the way to find A330 which is a natural fit for GF. Also plans are to phase out the A340 later (in a few years), replace them with A330 so prior to the new 787 arriving Gf will have one aircraft type for its widebodied flying. Makes the transition easier.