He announced initially announced the awards last Tuesday in a Tweet.
"I will be announcing THE MOST DISHONEST & CORRUPT MEDIA AWARDS OF THE YEAR on Monday at 5:00 o'clock", Trump tweeted.
The White House hasn't given much indication if the awards will actually happen.
Directing his words to Trump, he added: "Personally, I'm excited for your Dishonest & Corrupt Media Awards. Stay tuned!" he said.
The 71-year-old said he would be handing out his "dishonest media" awards in various "fake media" categories, ranging from "dishonest" to "bad reporting".
It also says the Trump campaign did not expect to win the U.S. election and Trump himself was "befuddled" by the result, that he was angry A-list stars snubbed his inauguration, and that he found the White House "scary".
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Trump latest tweet comes amid a firestorm over an explosive new book about the Trump presidency, "Fire and Fury: Inside the Trump White House".
Trump has fired back against author Michael Wolff and Bannon, calling Wolff a "total loser", and referring to Bannon as "Sloppy Steve".
After sharing his excitement at the prospect of winning an award, the host of The Late Show revealed that he had purchased a "billboard in New York's City Times Square in hopes of increasing his chances of being honored in categories such as "Least Bretibarty", "The Eric Trump Memorial Award for Disappointment" and "Smallest Button".
At the bottom of the ad it reads: "The Daily Show with Trevor Noah is so fake even this ad isn't real".
It is unclear how Mr Trump's awards will be judged.