The 'Britain’s Got Talent’ judge, who previously starred alongside the ‘Cilla’ star in a 2013 theatre production of ‘A Midsummer Night’s Dream’, said she was like a ‘sister’ to him during an interview on ‘The One Show’.
"I feel a lot of compassion for Sheridan,” he told hosts Matt Baker and Alex Jones.
"I love Sheridan she is like a sister to me.
"She is obviously going through a very serious issue with her family - in any other job you would be allowed some time off, wouldn't you?
"I think she should definitely be allowed this time off."
David added: "We wish her all the best, audiences will be thrilled when she does come back.
"I've seen the show already, it's fantastic. I've got tickets again and can't wait to go again."
David’s words come after the 34-year-old actress was signed off from her role as Fanny Brice in ‘Funny Girl’ for a month.
The Savoy Theatre released a statement confirming Sheridan would be getting the “rest and support” that she needed during this “very difficult and stressful time”.
It continued: “We will all miss her enormously and send her our love and best wishes - and we are looking forward to her return in due course.”
It has been a particularly difficult couple of months for the star, who announced back in March that her beloved father had been diagnosed with cancer.
She was also forced to speak out on rumours that a performance of ‘Funny Girl’ had been cut short because she was drunk, more recently blasting the press on social media for their treatment of her at such a tough time in her personal life.
Writing on Twitter earlier this week, she said: “Well done press! U let me down, the cast and everyone who spent money to see me.”