"I played myself overseas in the non-professional era, and I know how good an experience it is.
"They haven't betrayed the country by going over there and having that experience. "Let's see if we can tell them how much we want them back."
The Reds desperately need an experienced playmaker, with current No.10 Jake McIntyre a good prospect but struggling to compete consistently at Super Rugby level.
Cooper would also provide additional back-up to Wallabies flyhalf Bernard Foley, who edged him out in a months-long battle for the position in the lead-up to last year's World Cup.
"I know how much he loves playing in Australia," said Wallabies captain Stephen Moore, who has also signed for the Reds next year.
"It'd be a great thing having him back playing here. If it can all be worked out it would be a great result."
Reds executive general manager Daniel Herbert said there would be room for Cooper at Ballymore if he was able to secure a release from Toulon.
"If the desire's there... we don't like to comment until things are solidifying, but there's obviously room," Herbert said.
"The state certainly is involved but I'm an unashamed fan of Quade, have been for a long time.
"I think he gets unfairly tarnished at different times.
"If he wanted to come back, we'd welcome him."
- AAP