Sportal.co.nz 20.May.2013Getty Images
Cooper, who labelled the Wallabies camp a toxic environment last season, was left out of Deans' initial 25-man squad on Sunday despite being one of the form players in Super Rugby.
The 38-Test playmaker could still feature in the three Test series in June-July, with a further six players to be added to the squad on June 11.
However, Cooper faces a seemingly impossible take to force his way into the Test line-up after Deans declared James O'Connor his first-choice flyhalf on Sunday.
But the coach is adamant the door is still open for Cooper and strongly denied suggestions he has a personal beef with the Queenslander.
"People will say 'well that's the end for Quade', but that's not the case," Deans told a packed press conference at the Museum of Contemporary Art in Sydney on Sunday.
"There are still six positions to be resolved and we all know Quade's history in the group.
"I've selected him on 38 occasions so he's had a lot of faith and support from me so that's not an issue, and to suggest otherwise is nonsense.
"He will get the opportunity to play against the Lions and we've had dialogue around what's important.
"He understands what's important at Test level and it's a great opportunity for him to press his claims."
Pressed on what specific aspects of his game he has told Cooper to work on, Deans challenged the 25-year-old to put his 92kg frame to better use in defence.
"Test rugby's another level from Super Rugby and we would like to see Quade defend in the front line," he said.
"We would like to see him 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 hopefully dent the Lions' belief at the same time, playing for the Reds."
Pressed on O'Connor's selection at flyhalf having played predominantly on the wing in his 37-Test career, Deans explained: "We believe he caters for our need. The last time he (played at number) 10 against Wales at the end of 2011 he did a very good job.
"He's just got the components that we're looking for. He's clearly a bloke that traumatises defence and he keeps the attack very square which provides opportunities for the channels around him.
"... The great thing is we've got a number of blokes who are capable of playing at Test level and it's just a matter of identifying the ones that we believe will serve the team's needs best, and in the first instance James has got that opportunity."
The chosen 25 will assemble in Sydney on June 2 to begin preparations for the series opener in Brisbane on June 22.
Brumbies veteran George Smith (knee) and Waratahs hooker Tatafu Polota-Nau (broken arm) have been ruled out of the series with injuries suffered on Saturday night, while Brumbies centre Pat McCabe is also in doubt with a knee injury.