Cooper and Morris have been ruled out for several weeks after both received results of scans yesterday.
Cooper is expected to be out between four and six weeks due to a facial injury, while Morris will be out for up to a month with a hamstring tear.
Both players suffered the injuries in Sunday’s hard-fought win over Wests Tigers at Kograh.
“Matt has fractured both his eye-socket and cheekbone as well as hand all at the same time and we have projected him being out 4-6 weeks,” said Dragons Performance Director Jeremy Hickmans.
“He will be going in for surgery on all his injuries on Friday and will know for more afterworlds.
“He got caught in the same tackle on both his eye-socket and cheekbone after he did his hand in the tackle before.”
Club staff are hopeful that Morris can make a return to action by round 16.
“Brett has a small hamstring tear and at the moment we are still saying he’s available for State of Origin selection,” added Hickmans.
“It just depends on what selectors want to do with him and training.
“He started training with us this morning and will have physiotherapist Andrew Gray with him moving into Origin if selected, so he would have that continuity throughout [the week].
“He could be training by the end of next week depending on how he responds to treatment.”