The British comic thinks his friend - who endured a stint in rehab last year following her split from husband Ashton Kutcher - would benefit from joining a group trip to The Ananda Spa in the Himalayas, a yoga retreat which promises to "cleanse the soul and heal internally" and offers meditation classes and healthy eating.
A source told The Sun newspaper: "Russell and Demi have become friends since she started his yoga class.
"He remembers how much yoga and meditation helped him after his split with Katy Perry and feels it will help Demi too.
"Spiritual retreats can be hard work, but if you're in the right frame of mind they're really beneficial."
Russell, 37, recently spoke of his friendship with Demi, which developed when she was one of a group of yoga fans who began practicing the technique at the 'Arthur' star's Los Angeles home, and though they have forged a close bond, he insists there is nothing romantic between them.
He explained: "Demi Moore, as far as anything more physical goes - she's just at yoga. I really like her, she's really lovely. I just see her at yoga. She's an older lady, she's incredibly beautiful but that's that.
"I like the yoga thing, it's the dawning of a wonderful new era. It's proving to be an interesting new phase for me - yoga, transcendental consciousness, meditation, good-looking people. It's the dawning of a new Sixties."
Former sex and drugs addict Russell was previously reported to have taken a yoga instructor's class with his own meditation guru Tej Kaur in the hopes of setting up his own "all-giving studio" to help the homeless and addicts in need of spiritual guidance.
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