"If the British Government guarantees its life, I think it's in his best interest to hand over to the authorities," Moreno said.
Ecuador said that the UK has given a guarantee, but Moreno said he needs clarification on the British position.
The British Foreign Office referred to a CNN question about how to find the home office.
Robert Mueller's investigation of Donald Trump's links with associates and Russian Presidential Elections in the 2016 presidential election. WikiLeaks posted thousands of emails stolen from Democrats by Russian agents during the election.
A Justice Department investigation of Assange and WikiLeaks dates at least 2010, when the site posted thousands of files stolen by the former US Army intelligence analyst now known as Chelsea Manning.
Moreno said he would prefer Assange himself because of the cost Ecuador is paying after granting him asylum as well as his own good.
"More than five years in asylum is not human," Moreno said in an interview with Carmen Aristegui for CNN en Español.
But he said Ecuador was not about to throw Assange out.
"We want to protect Mr. Assange's rights – this is why we are looking for a solution, but this needs to be agreed upon," he said.
Moreno said: "According to the British government, they would never extradite a person to a country where his life is at risk."
"He wants to spend a few months in jail, after that, freedom," Moreno said.
Assange faces a British arrest warrant over violating bail conditions by seeking asylum in the Ecuadorian Embassy in 2012, but Sweden, which has been seeking sexual abuse allegations, has said he is no longer seeking to extradite him.