Snowden, 37, has been in exile in Russia since fleeing the US after leaking highly classified information in 2013.
Trump said he was “very strongly” considering a pardon for Snowden, who worked for the CIA and National Security Agency for several years.
He said: “Many people think he should somehow be treated differently and other people think he did very bad things.
“I’m going to take a very good look at it.”
Before his election, Trump had called Snowden a “traitor” and a “spy who should be executed”.
He raised the issue last week after saying he had heard the leaker was being “persecuted”.
“People think that he is not being treated fairly,” Trump said. “It’s something I could look at.”
Snowden fled after being charged with spying and theft of government property.
He said the CIA and NSA had “hacked the constitution” by using large-scale surveillance.