Advocaat, who turns 70 in September, would become his country's oldest ever national coach, usurping Guus Hiddink, who was 68 when he left the job in June 2015.
Hiddink's successor Danny Blind, who was unable to lead the team to Euro 2016, was sacked in March in the wake of the 2-0 World Cup qualifying loss to Bulgaria.
Netherlands have suffered two defeats in their opening five Group A games and sit fourth in the pool, already six points behind leaders France and three behind second-placed Sweden.
Reports in Netherlands claim the appointment of Advocaat, who is currently employed by Turkish club Fenerbahce, will be confirmed as soon as the paperwork has been completed.
Royal Dutch Football Association technical director Hans van Breukelen will speak about the situation on Wednesday, according to De Telegraaf.
Advocaat has had two previous stints as national boss, from 1992-1994 and 2002-2004, and three as assistant coach, including most recently last year. Only Rinus Michels has had so many spells in charge.
Former Netherlands captain Ruud Gullit is reportedly set to be named Advocaat's assistant. Gullit won the last five of his 66 caps towards the end of Advocaat's first tenure, before a dispute over tactics in the build-up to the 1994 World Cup signalled the end of his international career.
Advocaat led Netherlands to the quarterfinals of the 1994 World Cup in the United States, where they lost to Brazil, and to the semifinals at Euro 2004, when they were knocked out by hosts Portugal.
As well as managing Netherlands and a host of European clubs -- including PSV Eindhoven, Rangers, Zenit St Petersburg and Sunderland -- Advocaat has also taken charge of United Arab Emirates, South Korea, Belgium, Russia and Serbia.