The relationship between the siblings and their parent is said to be at "breaking point", after the actress had allegedly ignored them for months.
Rumer, 23, Scout, 20, and 18-year-old Tallulah - whose father is Bruce Willis - are now looking into taking legal action against their mother following a recent series of arguments, according to RadarOnline.
A source said: "They made it clear to her weeks ago that they do not want to talk to her right now but she is still trying to contact them.
"Demi has been calling them incessantly and emailing them, leaving them tearful messages and begging them to call her and the girls are sick of it.
"It is a really drastic measure and not something they are considering lightly but they just feel like they want some peace and quiet.
"Demi is beside herself over the situation. They won't return any of her calls, emails or texts."
They added: "The girls have cut off all contact with Demi, and she is absolutely devastated by it. She has returned to work and is trying to hold herself together, but this is a really tough time for Demi."
It was previously claimed that the daughters had "broken all ties" with Moore, but it was later said that Moore was behind the lack of communication.
In a similar case, Courtney Love was handed a restraining order against her daughter Frances Bean Cobain in 2009.