Assange, 42, fled to the South American country's embassy in June 2012 to avoid extradition to Sweden to face allegations of sexual assault and rape, which he denies.
He says he fears Sweden could extradite him to the United States to try him for one of the largest information leaks in U.S. history if he agrees to go.
Ecuador, which has granted Assange political asylum, wants London to assure him safe passage to Quito. But Britain has surrounded the Ecuadorean embassy with police officers round the clock ready to detain him if he leaves it.
Ecuadorean Foreign Minister Ricardo Patino flew to London a year ago to meet his British counterpart to try to broker a deal. Both countries agreed at the time to create a working group to try to resolve the standoff.