Julian Assange expects to wait six months to a year for a deal to free him from Ecuador's embassy in London.
In an interview broadcast last night, the Wikileaks founder said he hopes Sweden will drop its case against him.
The former computer hacker has been staying at the embassy for more than two months, seeking to avoid being sent to Sweden for questioning over rape and sexual assault allegations.
Talks over Mr Assange's fate resumed this week, and Ecuador's government said it was optimistic it will be able to strike a deal with Britain for Mr Assange to receive guarantees he would not be further extradited from Sweden to the United States.
Ecuador granted him asylum earlier this month saying that it shares his fears that he could face charges in the US over the publication in 2010 by WikiLeaks of thousands of secret US diplomatic cables.
"I think the situation will be solved through diplomacy ... The Swedish government could drop the case. I think this is the most likely scenario.
“Maybe after a thorough investigation of what happened they could drop the case," Mr Assange told Ecuador's Gama television network.
"I think this will be solved in between six and 12 months; that's what I estimate," he said in the interview, which was recorded earlier this week inside the embassy.
Britain says it is legally obliged to extradite Mr Assange to Sweden, and that it will not allow the 41-year-old Australian to leave the embassy and travel to the South American country.
Ecuador's Foreign Minister Ricardo Patino said on Wednesday he was optimistic the British government would agree to give Mr Assange written guarantees that he would not be extradited from Sweden to any third country.
Ecuador has said that if Assange received such assurances, he would decline its offer of asylum and hand himself over to Swedish prosecutors.
Asked during the interview if he could travel to Sweden under those conditions, he was non-committal.
"At some point, if the way has been paved ... it would not be correct to hold me in prison [in Sweden] without charges."
He did not mention the allegations of rape and sexual assault made against him by two WikiLeaks supporters in 2010.
A veiled British threat to enter the embassy to arrest Mr Assange angered Ecuador's President Rafael Correa. But the leftist leader said last weekend that the threat had later been lifted and he considered the "unfortunate incident" over.
In another sign of thawing tensions, Ecuador's Vice President Lenin Moreno met British Foreign Secretary William Hague on Wednesday, but any deal looks likely to take time.
"Given Ecuador's position on what they call diplomatic asylum and our very clear legal position, such a solution is not in sight at the moment," Mr Hague told the BBC yesterday.