The 16-year-old fashion designer is said to be considering living with her dad, personal trainer Carlos Leon, after a series of arguments with her popstar mother.
A source told Grazia: "They have been arguing like crazy. But Madonna would far rather try to sort things out than for Lourdes to leave home and move in with her father. She's not happy about it, but Lourdes seems to have her mind made up."
Madonna - who also has son Rocco, 12, with ex-husband Guy Ritchie and adopted children Mercy James, 6, and David Banda, 7 - recently cancelled a planned Australian tour, saying that she wanted to spend more time with her family.
Arguments between the singer and her daughter have been said to range from Lourdes's choice of friends to her relationship with Madonna's 24-year-old boyfriend Brahim Zaibat.
After Lourdes had been caught smoking earlier this year, Madonna said: "It's hard - every day is a negotiation. But cigarettes I'm not very fond of for anyone, especially my daughter."