Graham said he had full confidence in the Wallabies vice-captain's ability to defend strongly in the No10 channel in 2014, and the recent Wallabies' spring tour showed his worth.
With Israel Folau a standout at No15 for Australia in the five tests in Europe, Cooper stayed in the front line and muscled up.
"I thought he did a really good job in the frontline," said Graham, an assistant to ex-test coach Robbie Deans in 2009-10.
"I toured with Quade with the Wallabies in 2009 and he played inside centre on that grand slam tour and defended really well."
While the Reds' best pack for their competition opener against the Brumbies on February 22 looks mostly settled, the three-quarter line is wide open, highlighted by Harris, Ben Tapuai, Anthony Fainga'a and Chris Feauai-Sautia fighting for two centre spots.
Hooker James Hanson (illness) is the only Queenslander unavailable for Saturday night's opening trial with all recent test tourists set for a major hit-out against the 2012 and 2013 champions.
- AAP