I would think with 767 experience its more than likely you will go 777, especially if your coming from the USA, as the system there to get into these positions usually means your overall experience is generally higher than those in a similar position coming from Europe.
Just for your info and a little background, those that were told they would be on the 777 and ended up on the 320 had Boeing experience yes (some widebody, some not), however their overall total time was around 1500 hours (and less) in some circumstances, that tied with a spate of heavy landings on that fleet mean't they re-evaluted where guys ended up, some 320 some 330, again dependant on total hours.
At the time it seemed to be around 3K total and over went wide body those under went to 320, not everyone but most. Also factored into this was the massive delay in waiting for the simulator (3+ months) to complete type ratings, they needed guys elsewhere so changed them, fair enough in my eyes, some guys felt screwed over and for some rightly so, as they were promised one thing, gave up their position in a comfortable company and then once arrived were given another and yes that does hurt!
Nothing is a given here, sometimes its luck, but there are no guarantees!