Snowden was on a flight from Hong Kong that arrived in Moscow Sunday and was booked on a flight to Cuba Monday, the Russian news agencies ITAR-Tass and Interfax reported, citing unnamed airline officials.
"We know that he's currently in Moscow, and we are ... in touch with the highest authorities of Russia," Patino said.
Anti-secrecy group WikiLeaks said Snowden was bound for Ecuador "via a safe route for the purposes of asylum, and is being escorted by diplomats and legal advisers from WikiLeaks." The organization's founder Julian Assange, was granted asylum by Ecuador last year and has been staying at the country's embassy in the United Kingdom.
The Russian reports said a plane carrying Snowden arrived in Moscow on Sunday and he was booked on a flight to Cuba on Monday. The reports cited unnamed airline officials and said he intended to travel from Cuba to Caracas, Venezuela. There was also speculation that he might try to reach Ecuador.
Snowden had been in hiding in Hong Kong for several weeks after he revealed information on the highly classified spy programs.
Patino said Ecuador would not base its asylum decision on its potential to damage the country's relationship with the United States
"There are some governments that act more upon their own interests, but we do not," Patino said. "We act upon our principles."
He added, "We take care of the human rights of the people."
Patino was to hold a news conference Monday evening in Hanoi.
WikiLeaks said it was providing legal help to Snowden at his request and that he was being escorted by diplomats and legal advisers from the group.
Assange has spent a year inside the Ecuadorean Embassy in London to avoid extradition to Sweden to face questioning about sex crime allegations. He told the Sydney Morning Herald that his organization is in a position to help Snowden because it has expertise in international asylum and extradition law.