Foreign Minister Maria Fernanda Espinosa said Ecuador was looking at the possibility of a third country or a personality stepping in to settle the five-year impasse.
Assange, an Australian citizen now aged 46, moved into Ecuador's embassy to avoid arrest over a now-dropped Swedish investigation into rape allegations.
He has not stepped foot outside the mission since, fearing he could be extradited to the United States and put on trial for WikiLeaks' publication of leaked secret US military documents and diplomatic cables in 2010.
British police have said they are still seeking to arrest him on for failing to surrender to a court after violating bail terms.
"No solution will be achieved without international cooperation and the cooperation of the United Kingdom, which has also shown interest in seeking a way out," Espinosa said in Quito.