Cooper hasn't been included in Robbie Deans' 30-man training squad for this weekend's get together in Sydney, heightening speculation that he won't be needed for the three-Test series with Warren Gatland's tourists in June and July of this year.
But Genia insists Cooper is the man he wants to share half-back responsibilities with against Britain and Ireland's elite, insisting that his Reds team-mate would get his nod at No10 over the likes of James O'Connor, Christian Lealiifano, Matt Toomua, Berrick Barnes and Kurtley Beale.
"I wouldn't want to play with anyone else. We've got such a good understanding," said Genia, whose partnership with Cooper was a major factor in the Reds' Super winning season in 2011 and the Wallabies' Tri Nations triumph the same year.
"The big thing with us is just the trust. We back each other to make the right play."
Cooper's omission has been met with surprise by a number of former Wallabies and a large section of the Australian press but it doesn't mean he definitely won't be involved this summer.
There are still just over seven weeks until Deans takes a 25-man squad into a three-week training camp prior to the opening international against the Lions and Genia is convinced Cooper will be among that number come the beginning of June.
"If he's playing well enough, he's going to be there," added Genia.
"I think Quadey has been outstanding for us at the Reds.
"As we've seen with his attitude and demeanour this year, he's a new man and he's different.
"Last year is last year and we've moved on."