The Associated Press quoted Ecuador President Lenin Moreno as saying on the sidelines of the United Nations General Assembly meeting in New York on Wednesday, "we are likely to have a solution to the problem in the medium term".
"The British Government has told me that there may be an alternative," he said. "It is an issue that we have decided to keep in reserve with the British government and I want to respect that."
Reports in July said that Ecuador President Lenin Moreno had either finalised, or was about to finalise, an agreement with the UK to end asylum protection for Assange. But nothing has eventuated since then.
Ecuador has blocked Assange from using the Internet since the end of March, after he criticised alleged human rights abuses by Spain at the time when Catalonia launched protests for independence.
Moreno stressed that Assange was not an official at the Ecuadorian embassy in London. In response to reports that claim Ecuador considered sending Assange to the Ecuadorian embassy in Moscow in 2017, he replied that this could have been one of the possibilities.
"I understand that a wide range of alternatives was open, of possibilities, and I could have been among those, but it was not decided by that," he said.
He said, "unfortunately" the issue could not be resolved at the time.
"It is a problem not only because of the presence of Mr Assange in the Ecuadorian embassy, but also because of our respect for human rights. Being a refugee for five or six years in an embassy violates their human rights," Moreno said.
The Ecuadorian president said Assange had no Internet access, which was cut off in March when Assange expressed his opinions about the Catalan separatist conflict in Spain.
"I understand that (Assange) does not have that kind of services precisely to prevent him from doing it again," Moreno said.
"But if Mr Assange makes the commitment not to participate in this type of opinion about the policy of brother countries, as it has been with the American policy or Spain, then at that time we would have no problem in which he can continue to use these mechanisms."
The Assange saga began when he visited Sweden in August 2010 to attend a conference where he was scheduled to give a talk. During that visit, he had sex with two women whom he met. The pair filed rape and molestation complaints against him later, claims that he denied.
He was questioned by Swedish authorities and cleared. He could have left the country then and there, but stayed for a while, in case the authorities decided to question him again.
Interpol issued a Red Notice for his arrest on 20 November 2010. On 27 November, Assange surrendered to authorities and appeared before a Westminster judge. He was granted bail in December after his backers provided £240,000 in cash and sureties.
A legal back and forth eventuated and went on until June 2012, when Swedish prosecutors sought his extradition.
Assange's lawyers, among them the world-renowned Australian Geoffrey Robertson, replied that if he agreed to the extradition request, then he could be flown to the US from there.
On 19 June 2012, he jumped bail and took refuge in the Ecuadorian embassy, seeking asylum in the South American country. British police surrounded the building and blocked any chance of his leaving.
Ecuador granted him asylum in August 2012. He has had to stay inside the four walls of the embassy since then. He was granted Ecuadorian citizenship by a former president of the country, Rafael Correa.