She added that a third country might help out by offering Assange a new couch.
While Sweden has at least temporarily dropped that investigation, British officials say they'd still arrest him on charges of bail-jumping.
"I respect the situation he is in, which calls for respect of his human rights, but we also ask that he respects the situation he is in", Moreno said following his election to the presidency.
Foreign Relations Minister María Fernanda Espinosa said in comments reported by state media that it was "unsustainable" for Mr. Assange to stay at the embassy indefinitely.
Mr Assange, an Australian citizen, made headlines in 2010 when his organisation leaked USA military helicopter footage, which showed the killing of civilians in Iraq.
After living five years behind the safety of Ecuador's London embassy, Julian Assange may be in for a change of scene.
"No solution will be achieved without global cooperation and the cooperation of the United Kingdom, which has also shown interest in seeking a way out", she told foreign correspondents in Quito, according to Agence France-Presse. In 2016, a United Nations panel concluded that Assange had been "arbitrarily detained" and should be allowed to walk free. It said he should also be compensated for his "deprivation of liberty".
He also said that the risk of Assange being prosecuted in the USA has increased "in recent months under the Trump administration's war on WikiLeaks".
At the time, Ecuador said the United Kingdom should guarantee him "safe passage" to Ecuador if he leaves the embassy.