According to Metro, the singer has repeatedly telephoned Moore to give her support after she announced her decision to part from Kutcher.
"She is calling Demi almost every day and sends her messages telling her to be proud of her strength and to know that she fought to make her marriage work," a supposed friend told the newspaper.
"Madonna has had many younger boyfriends so she understands their mindset."
They added: "She has told Demi that Ashton's immaturity is evident and that she deserves someone who will fulfil her intellectually and emotionally."
It was recently claimed that Moore decided to divorce Kutcher after consulting with a psychic.
> Demi Moore 'fragile and alone' without Ashton Kutcher
> Demi Moore 'wants to punish Ashton Kutcher in divorce'
Moore and Kutcher have reportedly been attending marriage counselling sessions together at a friend's home.
It has been suggested that the couple were "fed up with each other" before Moore announced their separation.
Kutcher, who has been accused of infidelity, said in an interview given before the split was made public that he could "could never be with a woman who felt like she needed to change me".