The former Celtic and Hibs star has been without a club since leaving Falkirk at the end of the season.
He has been enticed down under by former Raith Rovers front man John Baird who is player-manager at the club based near Perth in the west of Australia.
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Hide AdMandurah play in the WA State League 1 and have qualified for the State League Finals series. They have four fixtures remaining with the club confirming he will play in the final two home games.
Baird told the Scottish Sun: "Leigh is a friend of mine and he's coming over for a holiday and a look round.
"I think he has some family nearby so he's eager to come over and see everyone and have a look at the club.”
Griffiths has been working during the off-season to get in shape as he looks for a new club.
Last summer he extended his Celtic deal by a season before moving to Dundee on loan. The stint at Dens Park was cut short with Griffiths agreeing to end his Celtic contract early.


The club said: "Mandurah Head Coach John Baird is thrilled to have completed the services of the Scotsman for the remainder of the year.
"Leigh is undoubtedly one of the biggest signings in not only Mandurah’s history, but one of the biggest in Australian NPL & State League football history."
Mandurah City president Nigel Mann added: “It sums up where the club is currently at and the hard work we have put in over the years.”