John Oliver
John Oliver (pictured above) and Jessica Williams were among the first names mentioned to replace Jon Stewart on "The Daily Show." Unfortunately, they've both taken themselves out of the running. Reuters

It's been a little more than a week since Jon Stewart announced that he will be stepping down as host of "The Daily Show" by the end of 2015. Many have begun to speculate as to who will fill the chair as host of the iconic late-night show. Demand for Comedy Central to get the new host casting right has already prompted two of the first choices on everyone's list to gracefully bow out of the court of public opinion.

When Stewart went off to direct the movie "Rosewater," John Oliver stepped in to guest host the show for a very successful summer, as Splitsider notes. Although Stewart has hosted the show for almost two decades, fans were quick to accept Oliver's style of reporting the fake news. This put him on the tip of most fan's tongues to replace Stewart. Unfortunately for "The Daily Show With John Oliver" hopefuls, his time guest-hosting the Comedy Central hit was good enough to land him his own show on HBO - "Last Week Tonight."

While leaving HBO for the established brand that is "The Daily Show" wouldn't necessarily be unfathomable, it's definitely not going to happen. Just days after Stewart announced his departure, HBO revealed that it had renewed Oliver's weekly satire news show for two more seasons (35 episodes total), according to IGN.

Stewart's lack of a clear end date, coupled with the timing of HBO's "Last Week Tonight" renewal, has led sites like Deadline to speculate that Oliver was Comedy Central's first choice for the role, but Oliver opted to stick with HBO for whatever reason. The final nail in Oliver's "Daily Show" coffin came from the president of Viacom Entertainment Group, Doug Herzog. When asked by the Associated Press if Oliver was being considered for the role.

"John Oliver's got a job," he said (via The New York Times). "I think he's spoken for."

With Oliver out of the running, many fans next hopes were for Jessica Williams, the 25-year-old comedian who started with the show covering the 2012 campaign trail. The youngest and first black female "Daily Show" correspondent quickly made a name for herself with her hilarious in the field reporting and on stage segments alongside Stewart, according to Glamor. With the long-time host leaving the show, many were quick to notice what a progressive choice it would be to give the chair to the in-house hire that's broken the most barriers in her time. After all, the upcoming movie "Hot Tub Time Machine 2" already named her as the host of the show in 2025, according to USA Today.

Unfortunately, like Oliver, Williams has removed herself from the hosting debate as well. In a series of Tweets on Sunday, compiled by Salon, Williams explained that, while she'll stay with the show, she feels unqualified to host "The Daily Show" at only 25-years-old. When Stewart took the chair following Craig Killborn in 1999, he was 37.

With Williams and Oliver out, it's really anyone's guess as to who is qualified to take over for the incomparable Stewart. Following its practices for the promotion of Stephen Colbert and Larry Wilmore, Comedy Central seems to like to hire from within its own ranks. For that reason, long-time correspondents Samantha Bee and Jason Jones are now the apparent front runners. Still, that hasn't stopped fans from speculating about a few more outside the box choices.

With speculation running so high, the International Business Times ask our Facebook followers to cast their vote for the next host of the show, prompting them with names like Alec Baldwin, Amy Schumer, Aziz Ansari and John Hodgman.

Many suggested their own personal favorites like comedians Aisha Tyler and Bill Burr, and one user even went as far as to suggest Mathew Perry. No official word has been made by Comedy Central about who the network is thinking of going with now that the most immediate choices are out of the running. In the meantime, fans have several more months left with Jon Stewart at the helm of "The Daily Show."