The club have offered the job to the Hunter Mariners coach, who only needs to say yes to succeed Dean Bell - who moved into a youth development role recently.
Leeds are understood to have agreed terms with Murray, who also coached successfully with the Illawarra Steelers and also Fiji in the 1995 World Cup. The only possible snag is that the Mariners - finalists in the World Club Championship this year but doomed to extinction when the two competitions in Australia merge - have not yet been pronounced dead.
"Australian Super League have agreed to his release once the future of Hunter is settled," the Leeds chief executive, Gary Hetherington, said. "A decision was expected at the weekend but now it seems it will be later in the week. Graham fits our bill and is keen to join us. We are confident of being able to announce his appointment later this week."
The appointment will end speculation that the Test coach, Andy Goodway, is lined up for the Headingley job, or that another former Great Britain coach, Ellery Hanley, is set to return to his home-town club.
Wigan have told London Broncos that they are not prepared to part with Henry Paul, but they are prepared to loan fringe players to Orrell rugby union club.
Salford, who have already signed four new players for next season, are interested in the New Zealand-born winger, Richard Henare, who was sacked by Warrington for disciplinary reasons last season.
Abolishing relegation from Super League will be among the measures to be discussed by the Rugby League Council when it meets next week.
The fate of Workington and Oldham after taking the drop has strengthened opinion that Super League clubs need time to plan ahead and achieve financial stability. The change would not initially be at the expense of promoting teams from the First Division, as Super League is projected to increase from its present 12 sides.
"The idea is for the present Super League clubs to be able to plan ahead and work without the fear of relegation at the end of the season," Peter Rowe, the Rugby Football League's media manager, said. "It should enable them to put a sound financial base in place before franchising operations come in in 1999."
The meeting will also discuss how competition outside Super League should be organised next season - one division or the present two - and the increasing likelihood that next season's World Cup will be postponed for a year.Reuse content