Assange is fighting extradition to Sweden to face the charges while staying in Ecuador's embassy in Britain.
The Australian has argued extradition to Sweden is a pretext for him to be sent to the United States, where authorities were angered by WikiLeaks' 2010 release of 391,832 secret U.S. documents on the Iraq War and 77,000 classified Pentagon documents on the Afghan conflict.
Ecuador granted him asylum, saying his human rights would be violated if the United States sentenced him to life in prison or the death penalty for alleged espionage.
Assange told Telesur television he believes Sweden will drop the charges of sexual molestation in which two women allege he coerced and raped them in 2010.
"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," Assange said. "I think this will be solved in between six and 12 months."
Britain's Foreign Secretary William Hague admitted he thought "a solution is not in sight" to the stalemate, The Daily Telegraph reported.