President Trump said Thursday morning that he believes the New York Times may have written the anonymous op-ed that claimed to be from a current federal official who said he or she and many others were working "diligently" to stop the president's "worst impulses."

"I think a lot of leaks are not leaks, they're made up by newspapers. The media is very dishonest," Trump told Fox News on Thursday morning. "The media is very, very dishonest, beyond anything anybody can understand. Now even the letter written to the Times, there is a chance, I don't say it's a big chance, but there is a very good chance that was written by the Times."

The Times published an anonymous op-ed in early September that described members of the Trump administration working against parts of his agenda. The author claimed not to be working alone and said the group is acting because they believe their primary duty is to protect the country.

A number of high-ranking administration officials immediately denied writing the op-ed.

Vice President Mike Pence and Secretary of State Mike Pompeo both denied on authoring the op-ed, and said the author should be ashamed for writing it. Treasury Secretary Steven Mnuchin, Director of National Intelligence Dan Coats, Defense Secretary Jim Mattis, and Housing and Urban Development Secretary Ben Carson all joined Pence and Pompeo in claiming they did not write the story. Outgoing U.S. Ambassador to the U.N. Nikki Haley wrote an op-ed defending the president.

The president floated the possibility that the op-ed was written by one of the thousands of officials that can claim senior-level status.

"And if it wasn't (the Times), it would be a low level, thousands of people qualified for that heading," Trump said. "And the Times said, 'we did scrutiny and we found out who this person was.' That means it is not a major player, because they know all the players, they know who they are. I wouldn't be that surprised because the Times is totally corrupt and dishonest. I wouldn't be surprised, what they write, forget it. Every day I have articles, every single day."

[Also read: Cloud of suspicion over Haley resignation as identity of 'Anonymous' mystery intensifies]