Cooper was left out of the last national squad but has been in sparkling form ever since, while Genia has quickly found his feet after a nasty knee injury saw him sidelined between September and March.
Genia is a near certainty to start the first Test at the Suncorp Stadium on June 22 and Mortlock is convinced he should do so alongside the player he has repeatedly said he feels most comfortable with.
"Whenever the Wallabies have done really well, it has hinged on a really strong halves combination," Mortlock told the Courier Mail.
"'Combination' is the word and Quade and Will have just played so much rugby together.
"To me, Quade has responded well to being left out of that last Wallaby camp.
"His form for the Reds is up and how he's talking off the pitch says to me he is in a good mindset."
One of Cooper's main rivals for the fly-half berth, Rebels utility star James O'Connor, has also impressed his former team-mate with his efforts this term but Mortlock doesn't believe his talents are best utilised at No10.
Instead, Mortlock would pick O'Connor on the wing, giving him the freedom to roam and therefore provide Robbie Deans' side with another playmaking option from second phase.
"James is a freakishly talented player and you want him having maximum impact," added Mortlock, who also reckons Deans must find the right balance between youth and experience this summer.
"I like the idea of him playing as a winger who can roam and get into first receiver too because all those benefits of him playing No10 can then come through.
"The debate about selections is very interesting across the whole team because the Wallabies will come into the first Test short of a gallop and the Lions will have an extended lead-in. It does potentially change the names and the way you might pick the Wallabies first up.
"The selectors have a real balancing act to reward some uncapped guys like an Israel Folau or Jesse Mogg, who are in impeccable form, but also backing experienced, big game performers.
"A lot of uncapped players are really producing strong Super Rugby performances but you have to go into a first Test this massive with more known factors than unknowns."