"You know I believe that it is premature to discuss this," Putin said in the second half of a two-part interview with German mass circulation daily Bild.
"We gave asylum to Mr Snowden, it was more difficult than giving it to Assad," he said, referring to fugitive US intelligence leaker Edward Snowden, granted asylum in Russia in 2013.
"First one needs to give the Syrian people an opportunity to have their say," Putin said, according to a Russian-language transcript of the interview published by the Kremlin.
"And I assure you that if this is done in a democratic way, then maybe he won't have to go anywhere. And it does not matter whether he is president or not."
Global powers are seeking to push the Syrian regime and opposition to the negotiating table in a bid to end the nearly five-year war that has killed 260,000 people.
Signup to our newsletter and follow us on Facebook and Twitter!
A UN-backed plan foresees talks between the different sides starting on January 25, the establishment of a transitional government within six months and elections within 18 months.
Putin -- who launched a bombing campaign in the war-torn country on September 30 -- appeared to defend Assad, although he acknowledged the Syrian president had made "many mistakes" since the conflict broke out in 2011.
The unrest would not have escalated so quickly "if from the very beginning it had not been fuelled from abroad -– with a huge amount of money, weapons and fighters," Putin said.
"Assad is not seeking to annihilate his own population. He's fighting those who have come to him with arms," Putin added.
"And if the peaceful population suffers because of that then I think that it is primarily those who are fighting him with arms in their hands and who are helping the armed groups that are responsible for this."
The Kremlin strongman reiterated that the Russian military has also been helping the armed anti-Assad opposition.
"We are talking about hundreds, thousands of armed people who are fighting ISIL," he said, using an alternative name for the Islamic State group.
"We support both the Assad army and the armed opposition. Some of them have already publicly announced this, some prefer to remain silent but the work is ongoing."