Sharon is a panellist on the daytime chat show but was not present for filming on Monday (9 May), with her co-hosts sending their love to her and the whole Osbourne family.
Co-host Julie Chen said: "Sharon is not here today. There are many tabloid headlines of her and Ozzy, rumours and speculation that they have split up after nearly 34 years of marriage. Sharon understandably took today off and we are sending all of our love to her and to her family, and we ask that you do the same."
Meanwhile, rocker Ozzy told E! News that any reports his sobriety played a part in the split are untrue.
"I have been sober for three and a quarter years," he said. "I have not touched drugs or alcohol in that time. Any reports that I am not sober are completely inaccurate."
Reports emerged at the weekend that Ozzy had left the family home in Los Angeles and checked into a hotel after rowing with Sharon. There have been claims the marriage is over, while other sources have said it is only a temporary split and the pair will reunite.
The couple previously denied split reports in 2013, with a rep saying: "Of course they row but they are still together. The marriage is not on the rocks."
Ozzy, 67, met Sharon, 63, when she was just 18. They married in 1982 and have three children: Aimee, 32 Kelly, 31, and Jack, 30.
Follow us on Twitter @RevealMag for all your celeb, fashion and beauty news!