Deans, who will add six more players to his squad on June 11, also found places in his party for uncapped number eight Ben Mowen and his ACT Brumbies team mate Christian Leali'ifano, who plays at centre and fly-half.
But there was no spot for Cooper, who was Australia's first choice fly-half until he sustained a knee injury at the 2011 World Cup and last year fell out with Deans when he spoke of a "toxic" environment in the Wallabies camp.
"People will say that's the end for Quade but that's not the case," Deans said.
"There are still six places to be resolved and ... I've selected him on 38 occasions so he's had a lot of faith and support from me and to suggest otherwise is nonsense.
"He will get the opportunity to play against the Lions.
"Test rugby is another level from Super Rugby, we would like to see Quade defend in the front line and we would like him to assert himself physically in the game because it's an element you can't avoid at Test level.
"He's got a great opportunity to do that, and dent the Lions as well, playing for the Reds."
Cooper's opportunity will come when the Queensland Reds host the Lions in Brisbane on June 8.
Deans confirmed that James O'Connor, who has started just one Test at fly-half, would be his first choice number 10, describing him as a player who "traumatises defences".
Kurtley Beale, who finished last season as the incumbent fly-half, was also omitted after being suspended indefinitely to undergo treatment for "personal issues" earlier this month.
Deans said Beale's mental and physical condition would be monitored but that there was "no point in second guessing" whether he would be available.
"He's got a chance but clearly he has to get through that process, clearly it will be a watching brief," he said.
First choice hooker Tatafu Polota Nau, who broke his forearm playing for the New South Wales Waratahs on Saturday night, is unavailable, Deans said, and Stephen Moore and Saia Faingaa were named as the specialist rakes.
Openside flanker George Smith, who was set to return from international retirement, has also been ruled out after badly injuring his knee on Saturday with Michael Hooper and Liam Gill left to battle it out for the number seven shirt.
Centre Pat McCabe, another player injured in the Waratahs-Brumbies match, has a suspected posterior cruciate ligament tear but could still play a part, Deans said.
Former rugby league international Folau, who has played 12 games of rugby union since switching from the Australian rules code for this season, was rewarded for his fine form at fullback for the Waratahs.
Wingers Joe Tomane and Nick Cummins, who both made their Test debuts last season, were included while there was still a place for Digby Ioane, who is leaving Australia at the end of the season to play for Stade Francais.
Uncapped Brumbies duo Jesse Mogg and Nic White were also not included in the initial squad of players.
Full-back Mogg was the front runner for inclusion in the squad after some scintillating early season Super Rugby form.
Scrum-half White had been widely tipped to back up Will Genia for the series, though still may get a chance with the Queensland Reds player the only specialist number nine named in the initial squad.
Deans said there would be at least one half-back added to the squad with Luke Burgess, who is currently playing in France, also coming into the reckoning.
"There is a lot of competition, this has been our most difficult process for a long time," Deans said of his squad.
"It's been selected to win. Period."
The Lions play the Barbarians in Hong Kong on June 1 and arrive in Australia the following day.
Backs: Israel Folau*, Digby Ioane, Joe Tomane, Nick Cummins, Adam Ashley-Cooper, Rob Horne, Pat McCabe, Christian Leali'ifano*, Berrick Barnes, James O'Connor, Will Genia.
Forwards: Wycliff Palu, Michael Hooper, Liam Gill, Scott Higginbotham, Ben Mowen*, Rob Simmons, James Horwill, Sitaleki Timani, James Slipper, Ben Alexander, Benn Robinson, Sekope Kepu, Stephen Moore, Saia Faingaa.
* Denotes uncapped player