In an exclusive interview in the Peruvian capital Lima, Correa said Assange's health concerns could worsen dramatically if his now five-month long stay in the embassy goes on for much longer.
"I haven't spoken with him since he arrived at our embassy, but the ambassador informed me that he is suffering from a slight problem in his lung -- nothing too serious," Correa, who was in Peru for a Latin American summit, told AFP.
"But there is still the danger that his physical and mental health could worsen, seeing that he is shut up in a small space, and unable to exercise in the fresh air. That would complicate the health situation of anyone," Correa said.
Assange has been sheltering in Quito's embassy to avoid extradition to Sweden for questioning on allegations of rape and sexual assault
Assange has strongly denied the allegations.
Assange fears that if he is extradited to Sweden, he eventually could be delivered to the United States for prosecution, where he could face a lengthy prison term or even the death sentence.
WikiLeaks enraged Washington in 2010 by leaking hundreds of thousands of classified US documents on the wars in Iraq and Afghanistan and embarrassing diplomatic cables from US embassies around the world.
Assange was arrested that same year in London but eventually was released on bail.
Ecuador granted Assange asylum on August 16, but Britain has refused to grant him safe passage out of the country - leaving the two governments in diplomatic deadlock and Assange stuck inside the embassy.
Talks to end the impasse have proved fruitless so far, but Correa said a breakthrough is still possible.
"We're not negotiating on the basis of human rights -- that term has not been used in this case. But there have been ongoing conversations" to resolve the case, he said.
"The solution to this problem is in the hands of Great Britain, Sweden and the European judicial authorities," said Correa.
"If Britain gives him safe passage tomorrow, this whole thing is over," he added.
Speaking about political matters back home, Correa left open the possibility that he will stand for a third consecutive presidential term.
"I have never been interested in political power, but situations where there is so much injustice, as with Ecuador's socio-economic poverty, can only be fixed by political means," said Correa, 49, whose term as Ecuador's president is due to end in May.