The 70-cap Wallaby has been frozen out of the Reds by coach Brad Thorn but remains one of the country's highest paid players despite playing third-tier club rugby in Brisbane.
Genia, who once formed a formidable halfback partnership with Cooper at the Reds and the Wallabies, said Rebels coach Dave Wessels was targeting his former team mate.
"I know Dave is definitely keen on him and wanted to have a few conversations with him," said Genia, who moved back to the Rebels this season after a stint in France. "Hopefully they can come to some sort of agreement.
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"He's a world class player.
"To have someone like that in the playmaking role at the Rebels would be huge.
"That's probably our biggest missing piece."
Despite an injection of Wallabies players from Western Force, the Perth-based team that was cut from the Australian conference of Super Rugby last year, the Rebels failed to reach the playoffs for an eighth successive season.
Wallabies utility back Reece Hodge took the number 10 shirt in the second half of the season after incumbent Jack Debreczeni struggled in the pivotal position.
The Rebels signed England-based Wallaby utility Matt Toomua for 2019 but he will not arrive until late in the season.
"Hodgey played 10 and played pretty well there but I think he's more of a centre," Genia said in comments published on Rugby Australia's website (rugby.com.au).
"So to have someone in the team who has won a title before and has had that success would make a huge difference."
Despite being an outcast at the Reds, 30-year-old Cooper has said he wants to remain in Queensland and regain his place in the Super Rugby side.
Former All Black Thorn has remained adamant, however, that the New Zealand-born player is not in his plans.
The standoff has left Cooper an expensive burden on the Reds' roster, with his contract worth an estimated A$650,000 ($467,000) per year and not set to expire until the end of 2019.
($1 = 1.3912 Australian dollars)
(Reporting by Ian Ransom; Editing by Greg Stutchbury)
