Madonna is waiting for a High Court judge's ruling on a dispute with ex-husband Guy Ritchie over the future of their 15-year-old son Rocco.
Mr Justice MacDonald analysed evidence about the dispute at a private hearing in the Family Division of the High Court in London earlier this month.
He is scheduled to deliver a ruling on Monday.
The singer and the film-maker are embroiled in litigation in England and New York.
Judges have heard that Rocco had remained in London with his father after a visit.
Madonna wants the teenager to return to live with her in the USA.
Lawyers have told Mr Justice MacDonald that Madonna wants to end legal proceedings she had launched in England.
The judge was asked to decide whether English proceedings should draw to a close or whether he should make decisions about Rocco's welfare.
Rocco and Mr Ritchie had been at the hearing but not Madonna.
The singer's lawyers told the judge that she had wanted to attend but was on tour in Australia.
Mr Justice MacDonald urged Madonna and Mr Ritchie to try to settle their dispute.
And lawyers told him that both Madonna and Mr Ritchie had outlined proposals for negotiation.