A judge is scheduled to oversee the latest stage of the dispute at a private hearing in the Family Division of the High Court on Monday.
News that Giggs and estranged wife Stacey were embroiled in a dispute emerged earlier this year.
Mr Justice Cobb considered issues relating to reporting of the case at a preliminary hearing in February.
The judge made an order limiting what journalists would be able to report – after an application by Giggs.
He said he would not allow reporting of financial information aired during the litigation.
The judge also said the pair’s children should not be named in any report of proceedings.
He said journalists could report that Giggs and Mrs Giggs were involved in a dispute – and name them.
Giggs had initially asked for an order preventing media representatives from attending hearings. He decided, however, not to pursue that application.
Mrs Giggs has asked for her privacy to be respected as the dispute unfolds.
Giggs retired as a player in the summer of 2014 and subsequently worked as United’s interim manager for a short spell.
He made a record 963 appearances for United over 24 seasons and won 64 Welsh international caps.