Assange, the WikiLeaks founder facing extradition to Sweden on sexual assault charges, has been staying in the Ecuadoran Embassy for more than a month after claiming asylum there.
The British newspaper The Independent said Assange might be able avoid extradition if such a meeting occurred.
Assange's supporters say they fear U.S. authorities are seeking to prosecute him for his involvement with WikiLeaks and would use his extradition as an opportunity to grab him, the newspaper said.
But Ecuadorean officials told The Independent they were also seeking assurances if Assange is sent to Sweden, he would not later be sent to the United States.
A senior legal adviser to the Ecuadoran government said embassy officials would protect Assange from that fate and would write to U.S. authorities asking whether the United States intends to seek extradition of Assange from Sweden.
"If Ecuador could be assured that the evil it wishes to prevent: the extradition to the USA of Julian Assange, could be [avoided], then that would be a just solution," the adviser told The Independent.
The WikiLeaks Web site has posted tens of thousands of internal U.S. communications dealing with defense and diplomacy, some of it classified, allegedly provided by a U.S. Army private.