Genia is a nailed-on certainty for selection and could captain the side for the three Tests in June and July, while fly-half Cooper's international prospects have been up in the air since he spoke of the Wallabies' "toxic" environment last year.
Only two years ago, the pair combined to scythe through a succession of Super Rugby defences as the Reds won the southern hemisphere's annual provincial competition for the first time.
They then teamed up for the national side to help Australia win the Tri-Nations for the first time in a decade, although they were less successful at the 2011 World Cup in New Zealand where the Wallabies finished third.
Both have since had knee reconstruction surgery and it is only in the last few weeks that they have been able to put together a sustained run of starts together.
Genia admitted the combination was still some way short of its very best but was quite clear who he preferred standing outside him in the number 10 shirt on match day.
"I love playing with Quade," Genia, who has played with Cooper since their schoolboy days, said in Brisbane. "We've got a long relationship. We've played together for a long time - I really enjoy that combination.
"More than anything it is a trust thing. In whatever decision each makes we back and support each other."
The fly-half position looks to be one of the trickiest for coach Deans to fill, especially since he has made it clear he will not want to blood untried players in what he considers the ultimate test in international rugby.
That would seem to rule out the likes of in-form but uncapped ACT Brumbies Matt Toomua and Christian Lealiifano, as well as former sevens skipper Bernard Foley.
Kurtley Beale finished last season as incumbent in the position but has just returned to action after being banned for hitting two team-mates and is more likely to be preferred at full-back.
Like Beale, Berrick Barnes played both fly-half and full-back for the Wallabies last year and filled the playmaker role in all three Tests as Australia swept Wales 3-0 in the June series.
The 26-year-old, who offers a more orthodox and structured option than Cooper, is short of match practice having just been declared fit after missing six weeks with a broken wrist he sustained in his only match of the season.
Equally versatile, and some would argue more talented, is James O'Connor but he has mostly been used in the back three by Deans and has played just one Test at fly-half.
That leaves Cooper, who has started 27 times in the Wallabies number 10 shirt, as by far the most experienced fly-half available.
Regardless, the mercurial 25-year-old was left out of a 30-strong squad for a planning camp for the Lions tour last month and Deans has been less than effusive when discussing him.
There is also a school of thought - centred mainly but not exclusively on his homeland of New Zealand - that Cooper has been "found out" by international defences and will never be the same threat he was in early 2011.
Adding to the doubts surrounding him is the fact that Cooper stands at full-back when the Reds are defending - a dispensation Deans is thought unhappy to continue at international level.
The first 25-man Wallabies squad for the Lions series will be named on May 19 with a further six players added when the Super Rugby season pauses for the international break.
Eschewing the outspokenness of last year, Cooper seems happy to let his performances for the Reds do the talking as he bids for a place in the party.
"It all depends on what the coach and the selectors are looking for," he said in Brisbane.
"Personally I am doing my best to work with Will, get the best out of each other and the Reds - I am not looking further than that."