Sharon and Ozzy Osbourne "talk every day".

Sharon Osbourne

Sharon Osbourne

The 'Talk' presenter split from her husband after 34 years of marriage last month amid claims he had been unfaithful with hair stylist Michelle Pugh and though she is still "disgusted" by the rocker, they are said to be slowly taking steps to repair their relationship.

A source told the New York Post newspaper's Page Six column: "They're not about to book a trip to the Maldives together but they talk every day. She's still disgusted by him."

Sharon - who is believed to be staying at the Beverly HIlls Hotel - has been receiving a lot of support, especially from her children Kelly and Jack Osbourne, and her 'Talk' co-host Sarah Gilbert.

The source added: "Sarah has really been there for Sharon, and the kids are firmly on Team Sharon, not Team Ozzy."

It was recently claimed the 67-year-old Black Sabbath frontman has been attending marriage counselling with Sharon and will do whatever it takes ro win her back.

A source said: "He wants his family back."

Ozzy has reportedly been grovelling to Sharon in a bid to regain her trust and affection following claims he'd been unfaithful to her.

The source added: "The Osbournes have been through thick and thin together and have stayed together through it all. This is putting them all through a really horrible time."

Sharon recently thanked her friends and family for supporting her through such a troublesome few weeks.

Speaking earlier this month, the TV star said: "I honestly cannot thank people enough for their backing me.

"For saying they love me. For everybody here at my home, supporting me, sending me messages of love. I honestly am empowered and I have found this inner strength and I'm like, 'Right. OK. What's next?'"

It has been reported that in addition to sleeping with Michelle for a prolonged period of time, Ozzy was also offering her financial support.

A source previously revealed: "Sharon found out about the affair by searching through Ozzy's emails. She was upset that he was supporting this woman!"