Kevin Blackwell will include midfielder Griffiths in the squad for this weekend's Yorkshire derby with Sheffield Wednesday at Elland Road if Leeds get international clearance in time.
Griffiths' previous clubs were Sydney United, Parramatta Power and Newcastle United in Australia's NSL.
He made his international debut against Jamaica in October 2005, scoring in a 5-nil victory, and he hopes the switch will help cement his place in Australia's 2006 World Cup squad.
He was also picked in Aussie coach Guus Hiddink's 23-man squad for the World Cup play-off with Uruguay in November, although he did not feature.