Cheney raised the possibility on "Fox News Sunday" that Snowden's motives in revealing the massive U.S. surveillance program were not so altruistic since he had absconded to Chinese territory.
"I am very, very worried that he still has additional information that he hasn't released yet, that the Chinese would welcome the opportunity and probably willing to provide immunity for him or sanctuary for him, if you will, in exchange for what he presumably knows or doesn't know," Cheney said.
"I don't think this is just a one-off disclosure," Cheney added. "I think there's a real danger here that he'll go beyond that."
Cheney said a major question about the Snowden affair was whether or not he was acting alone or if the information was given to him by someone else inside the National Security Agency. He told Fox he personally had doubts that a contract employee such as Snowden would have access to such sensitive material.
Cheney also said the Obama administration should take a firm and aggressive stance with China in order to get him into U.S. custody as soon as possible before he divulged more secrets to Beijing. "It depends, obviously, on whether or not the Chinese believes he still has value from an intelligence standpoint," Cheney said. "I've got to believe they will work that angle first before they decide whether or not they're going to turn him over."