Graham is the first US senator to connect Snowden with the Winter Olympics in Russia, reports Xinhua.
"I would. I would just send the Russians the most unequivocal signal I could send them," said Graham on Tuesday.
"We certainly haven't reset our relationship with Russia in a positive way. At the end of the day, if they grant this guy asylum, it's a breach of the rule of law as we know it and is a slap in the face to the United States," added Graham.
The 2014 Winter Olympics is to be held in Sochi, a city on the Black Sea coast, from February 7.
The US boycotted the 1980 Summer Olympics in Moscow, and four years later, the Soviet Union led the boycott of 1984 Olympics in Los Angeles, US.