According to a source, the two former The Osbournes stars have not even discussed divorce at this time, Peoplereported.
Other insiders have recently noted Sharon and Ozzy's split after 33 years of marriage may only be temporary, that it's possible they could still work through their issues.
News of Sharon and Ozzy's separation broke on Saturday, with subsequent reports claiming Ozzy had been cheating on his wife with a 45-year-old celebrity stylist named Michelle Pugh. Ozzy has reportedly moved out of the house and is currently living with a family member.
While neither Sharon, 63, or Ozzy, 67, has commented on the topic of infidelity, Ozzy released a statement refuting rumors that drugs played a role in their separation.
"I have been sober for three and a quarter years," Ozzy told E! News on Saturday evening. "I have not touched drugs or alcohol in that time. Any reports that I am not sober are completely inaccurate."
Sharon, a former judge on America's Got Talent, then skipped her appearance on Monday's episode of The Talk. Her co-host Julie Chen addressed the situation on TV by mentioning how tabloid headlines were circulating about the deterioration of Sharon's marriage and so she "understandably" took the day off.
"Sharon went ballistic with Ozzy and accused him of having the affair," a source told The Sun of London. "[Sharon] said she had suspected something had been going on for some time and now had proof."
Divorce rumors have plagued Ozzy and Sharon since 2013, but Sharon never denied the fact her marriage was often on the rocks. At the time of their wedding anniversary in July 2014, for example, they got into a huge fight and Sharon revealed she had reached her breaking point.
Sharon and Ozzy met in the early 1970s when he was a member of the band Black Sabbath. The pair wed on July 4, 1982 and later welcomed three children -- Aimee Osbourne, 32, Kelly Osbourne, 31, and Jack Osbourne, 30.
Everyone in the family, except for Aimee, starred on the MTV reality show The Osbournes between 2002 and 2005. Sharon later judged America's Got Talent from 2007 to 2012.