The last time the two players met was last month, with Muntari playing for Udinese against Grella's Parma. Muntari ended the game early, red-carded after exchanging blows with Grella. The incident earned the Ghanaian a two-match suspension.
For Graham Arnold's Socceroos, the friendly match on Tuesday is another step towards the Asian Cup next year.
Ghana's focus is on its hosting of the 2008 African Cup of Nations.
Both teams had impressive, but frustrating, experiences at the World Cup this year.
Australia's exit came after a controversial last-second penalty against a 10-man Italy, and Brazil disposed of the Africans with three unanswered goals in a game in which refereeing standards came under question.
Like Australia, Ghana surprised many observers in Germany with an energetic, hard-working style. The Black Stars emerged from tough group that included Italy, the Czech Republic and the US.
Chelsea's Michael Essien was outstanding against Italy, the eventual champions making hard work of a 2-0 win.
Ghana bounced back to beat the Czech Republic 2-0 and then controversially - referees again took centre stage - beat the USA 2-1 to qualify for the next round.
Australia last met Ghana in 1996, when goals from Paul Trimboli and Damien Mori made the difference for a Socceroos side that also featured Zeljko Kalac and Craig Foster.
Ten years later, Ghana are led by Frenchman Claude Le Roy, no stranger to Australian football.
The wandering Frenchman took Cameroon to the 1998 World Cup and put his hand up for the national team job five years ago, when Frank Farina was under fire.
Le Roy took the Ghana job after the World Cup and and has since led the team to impressive wins over Japan and South Korea
