The Times reported Some of the officials that were in the room told the publication no one really knew how to respond to the President’s comments.
One person reportedly suggested Mr Trump could host his show on weekends so as not to clash with Mr Limbaugh’s schedule.
But this wouldn’t work, according to the US President, as he had wanted the show to run daily for two hours at a time.
According to Mr Trump the only reason he had decided not to go ahead with it was because of the clash with the other radio show.
Mr Trump’s idea came just days before he announced a European travel ban as the coronavirus was rapidly spreading across the US.
At the time the US President said the restrictions were “strong but necessary”, calling the COVID-19 virus a “horrible infection”.
Apparently this wasn’t the first time he had brought up the possibility of creating his own radio show, the New York Post reported, with one the officials revealing people weren’t sure if it was a joke the first time he mentioned it.
Mr Trump has long been a fan of Mr Limbaugh, with the radio personality being one of his most relentless defenders.
The President invited him to his State of the Union address earlier this year, shortly after the radio host was diagnosed with advanced lung cancer.
This caused widespread controversy, with the radio host being accused of sexism, homophobia and racism throughout his career.
“Almost every American family knows the pain when a loved one is diagnosed with a serious illness. Here tonight is a special man, someone beloved by millions of Americans who just received a Stage 4 advanced cancer diagnosis,” Mr Trump said.
“This is not good news, but what is good news is that he is the greatest fighter and winner that you will ever meet. Rush Limbaugh, thank you for your decades of tireless devotion to our country.”
A bearded Limbaugh, seated next to First Lady Melania Trump who presented him with the medal, looked stunned as the president announced the award to the thunderous applause of republicans in the chamber of the House of Representatives.
Mr Trump said the award recognised the millions of people a day Limbaugh speaks to and inspires, as well as his charity work.