Stewart, who hosted the show for 17 years, recently announced his departure. His last episode is yet to be shot.
Williams, who joined 'Daily Show' in 2012, apparently topped the list of probable replacements of Stewart, reported the New York Daily news.
Former 'Daily Show' correspondent John Oliver and current correspondent Samantha Bee were also reportedly being considered for the post.
The 25-year-old comedian took to Twitter on Sunday to squash rumours.
"Fact 1: I'm not hosting. Thank you but I am extremely under-qualified for the job!" Williams tweeted.
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