Cooper was sent to the sin bin after 63 minutes for a high-tackle on Australia team-mate Berrick Barnes as the Reds claimed a 32-16 bonus-point win, their first over the Waratahs since 2003 as they clinched top spot in the Australian conference ahead of the Brumbies.
The reigning champions' success secured an elimination final against the Sharks next Saturday at Suncorp Stadium, but the Reds' ability to continue the defence of their crown could depend on the availability of Cooper, who is set to attend a hearing in Brisbane on Sunday.
The Reds have already had winger Digby Ioane suspended for five weeks for a lifting tackle on Sharks flanker Marcell Coetzee in March.
Following the win, their sixth in succession, Reds coach Ewen McKenzie said he was yet to view the tackle clearly, but believes the club's previous experience with Ioane could prove crucial in their bid to clear Cooper.
"I didn't get a good look at the tackle, but we have had to deal with one of these already this year so we will be vigorous in making sure we follow the process," he said. "It's not ideal but Quade has a clean record.
"I look back at the Ioane incident and how we managed that and it has been put in the experience bank.
"That will be front and centre with this one.
"We will make sure we dot our Is and cross our Ts."