"Sharon went ballistic with Ozzy and accused him of having the affair" with 45-year-old celebrity stylist Michelle Pugh, a source told the paper.
"[Sharon] said she had suspected something had been going on for some time and now had proof."
Ozzy, the former lead singer of Black Sabbath, is now reportedly living in a Southern California hotel.
Sharon first met Ozzy in the 1970s when her father managed Black Sabbath. Sharon later became Ozzy's manager.
The troubled couple, who got married on July 4, 1982, have three children together: Aimee, 32, Kelly, 31, and Jack, 30.
This isn't the first time Ozzy and Sharon have faced divorce rumors. "The Talk" co-host denied any problems in her relationship back in 2013 when rumors began swirling about the crumbling state of her union, but she did admit that her husband was struggling with substance abuse.
"He's been using alcohol and prescription drugs for the past year and a half. That's true. That's very true. Everybody knows he's been struggling with this his entire life," she said. "I never knew he was using prescription drugs. I knew he was drinking occasionally, but I didn't realize to the extent."
However, in 2014, Sharon seemed to reach a breaking point and confirmed strife in her marriage.
Sharon spoke to The Daily Mail about a serious fight she had with Ozzy on July 4 of that year — their 32nd wedding anniversary — which nearly destroyed the marriage.
"I would never have imagined our anniversary would be the start of one of the worst periods in our marriage," she said.
"I thought, 'I can't carry this anymore. It's what I have always done and I'm tired.' I said, 'I want a divorce.'"
But the couple managed to stay together, which is exactly what one source still believes could happen this time around.
According to People magazine, an insider believes it's "sort of true" they've broken up, but "he'll be back."
Hairstylist Michelle Pugh, who has worked with celebrity clients including Jennifer Lopez and Alicia Silverstone, has reportedly taken leave from her Los Angeles salon, Meche, due to a "personal emergency," the store's manager told The Sun. She has also canceled recent appointments.
Reps for Ozzy and Sharon have not yet commented on recent reports.