If Colbert hosts The Late Show, he would give up the conservative "Stephen Colbert" persona he uses on The Colbert Report, sources said.
Last September, The Colbert Report finally put an end to The Daily Show's 10-year winning streak at the Emmys, claiming the title of outstanding variety series for the first time.
Colbert recently came under fire for a satirical tweet and dedicated much of Monday's show to addressing the uproar he caused when he created a faux charity called "The Ching-Chong Ding-Dong Foundation for Sensitivity to Orientals or Whatever". A Twitter hashtag #CancelColbert was created in response.
Colbert insisted its creation was inspired by the irony of Washington Redskins owner Daniel Snyder's new charitable organisation, "The Washington Redskins Original Americans Foundation".
"Internet equality is more important than ever, as I learned this weekend when the interwebs tried to swallow me whole," he explained. "But I am proud to say that I got lodged in its throat and it hacked me back up like a hastily chewed chicken wing."
Colbert quipped: "Who would have thought that a means of communication limited to 140 characters would ever create misunderstandings."
Other names reportedly being considered for the hosting gig include Neil Patrick Harris and Craig Ferguson, according to Mashable.
E! Host Chelsea Handler has also recently been rumoured to be a front-runner for the position.
The brash blonde has become a household name, thanks to her E! late night show, but on Sunday she announced she was quitting the network when her deal expires at the end of the year.
And the timing did not go unnoticed, when David Letterman revealed he was retiring next year.
Rumours were rife over the internet as one tweet read: "David letterman is retiring, MY PRAYERS have been answered... They're a a slot open for you @chelseahandler" while another said: "WAIT. Chelsea Handler. Just. Quit. E!. You don't think..."
Handler, 39, known for her bawdy humour, counts Hollywood A listers Jennifer Aniston, Reese Witherspoon and Gwyneth Paltrow among her best pals - and has often had them on her show.
Appearing on Letterman's show last April, Handler and Letterman enjoyed some banter about Dave's job.
Discussing the shake-ups in late night TV, Handler said: "Nobody can keep their job for very long, it seems. I mean, you're lucky to have a job over here at CBS."
"I'm lucky to have a job, period," Letterman replied: "I don't care where - I'm lucky to have a job. Mowing lawns - I would be lucky to have a job mowing lawns."
Chelsea retorted: "Well, yeah - you're a small man."
Discussing Jay Leno's departure from NBC's Tonight Show, Handler - who had made it no secret she was unhappy at E! - joked that Leno had left her a voicemail. The odd couple's interview ended when Chelsea called him "dainty", and Letterman retorted: "You're kinda hefty for a broad."
Grabbing her chest, Chelsea, clearly not insulted, replied: "We all know what you're talking about."
Handler's manager Irving Azoff told The Hollywood Reporter: "Chelsea intends to leave when her contract expires. She hired me to figure out her life after E! We have at least seven suitors and many ideas."
"Chelsea has nine months left on her contract and E! will not comment on the future of Chelsea Lately at this time," a representative from the network said.
If Handler were to take over, she would be the first woman to have her own network late night show since Joan Rivers, who hosted The Late Show - then on Fox - for just one year between 1986 and 1987.
Bizarrely, new Tonight show host Jimmy Fallon - who could find himself going up against one of them - will have both Handler and Colbert on as guests on his NBC show next week.
- Daily Mail
