“Larry has fought so many health issues in the last few years and he is fighting this one hard too, he’s a champ,” a source close to the family told the network.
Mr King, who hosted Larry King Live on CNN for 25 years, and began his media career in radio has suffered a string of medical problems over the years.
In 2017 he announced that he had been treated for lung cancer and he had a major heart attack in 1987.
Mr King also underwent angioplasty in April 2019 and suffered a stroke in 2020.
His hospitalisation, which has lasted more than 10 days, was first reported by Roger Friedman’s Showbiz 411 website.
Mr King is in the process of divorcing wife Shawn King, but neither she not their two sons, Chance and Cannon, can reportedly visit Mr King in the hospital.
The broadcaster lost two children in 2020, son Andy, 65, from a heart attack and daughter Chaia, 51, from lung cancer.
An estimated 20.2 million Americans have now tested positive for Covid and more than 348, 000 have died from the virus.
Mr King’s representatives have not yet commented.