Barnes was named man of the match for his performance, largely at No.10, in Australia's 21-18 victory in the third-place playoff against Wales at the World Cup last month.
O'Connor, 21, has been keen to move in off the wing and play a more central role in the Wallabies backline and a match against the Barbarians has less riding on it than most internationals.
"He can ball play, he has shown that in Super Rugby (for the Western Force),'' Australian halfback Will Genia said.
"He really wants the opportunity and hopefully Robbie gives it to him.
"We will how see how he goes.''
The Wallabies have an enviable record against the Barbarians, having won eight of their 11 meetings.
The invitational side has chalked up major southern hemisphere scalps in the past two years, defeating the All Blacks in 2009 and South Africa in 2010.
- AAP