The duo suggested that Drudge is turning against President Donald Trump, pointing to what they claim are negative stories published by the Drudge Report.
Watters began the discussion by describing the Drudge Report as a "very fair, very aggressive, very bold" publication, but noted that it seems to be running negative stories about Trump.
He then compared the outlet to CNN.
"You know, that's what you log on to CNN.com for," he said.
"But it just seems like the website has recently played up Trump gaffes and downplayed his successes," he added.
Kurtz, a media critic, agreed with the host, arguing that Drudge -- who Kurtz claims to have covered since the early days of his career -- is now "primarily interested in clicks" which is why his outlet is publishing "largely anti-Trump" stories.
Echoing his initial comments, Watters asserted that the Drudge Report is now comparable to more mainstream news sources, agreeing with Kurtz that Drudge could be publishing articles critical of Trump because he is focused on attracting as many visitors to his website as possible.
However, Watters left open the possibility that the conservative blogger is changing his mind about the president.
"It's hard to tell whether as you said he's riding wave for clicks or there's something personally inside his heart and his mind that has shifted against the president," he said.
Kurtz toned down his criticism of Drudge, suggesting that the conservative media figure has to publish articles that can be interpreted as critical of Trump because he has to cover the House Democrats' impeachment probe fairly.
The media critic suggested, however, that Drudge turning against Trump could be a big sign of trouble, given how influential his publication is.
"You know people on the right say 'we're going start an alternative to Drudge' -- well good luck with that," he said.President Donald Trump's relationship with conservative media is not nearly as good as it used to be, according to reports. The president is allegedly growing increasingly frustrated with how his onetime favorite news channel, Fox News, is covering his presidency.
Earlier this summer, Trump -- who has long publicly blasted Fox News for "changing" -- reportedly contacted the network's CEO Suzanne Scott, complaining about unfair coverage. After a lengthy phone call, in an apparent effort to appease the president, Scott arranged an interview with anchor Bret Baier.
The reported arrangement does not seem to have helped, however, given that Trump has not stopped attacking some of the network's most prominent figures.