In an interview with the Spanish newspaper El Pais, Moreno said Ecuador was not helping Assange to exercise his rights by prolonging his stay in Ecuador's London embassy, and therefore had to find a way to end the impasse.
He said any solution would have to ensure Assange's rights, especially his right to life, while at the same time it removed what was obviously a problem for his country.
"The ideal way out would be to talk with Mr Assange and his lawyer in order to consult them if he is willing to accept the conditions under which the United Kingdom provides the possibility of an exit," Moreno said according to a Google translation of his interview.
Ecuador signed a security agreement with the US in May, a sharp move away from policies pursued by the previous government led by Rafael Correa.
The editor of The Intercept, Glenn Greenwald, wrote in last week's report: "It is thus highly unlikely that Moreno — who has shown himself willing to submit to threats and coercion from the UK, Spain and the US — will obtain a guarantee that the UK not extradite Assange to the US, where top Trump officials have vowed to prosecute Assange and destroy WikiLeaks."
In April, Assange lost a bid in court to get an UK arrest warrant against him dropped.
The WikiLeaks publisher has been taking refuge in the Ecuadorian embassy in London since June 2012.
His problems 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 of all accusations. 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. Bail was granted to him in December after his backers provided £240,000 in cash and sureties.
Then began a protracted period of legal back and forth that 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 recently granted Ecuadorian citizenship.