The former World Player of the Year has been sidelined since tearing ligaments in his wrist during the win over the Auckland Blues on April 13.
"Brodie's probably another three weeks away, so we're looking at probably the Reds," Cooper said ahead of the Chiefs' trip to Dunedin to play the Otago Highlanders on Saturday.
The Chiefs play the Queensland Reds in Hamilton on May 24.
Retallick's injury has compounded a tough season for the Chiefs, who have lost All Blacks fullback Damian McKenzie for the rest of their campaign with a knee ligament injury, which he also suffered against the Blues.
Cooper has also had to do without flanker Sam Cane this season as the All Black recovers from a broken neck sustained during a test against South Africa last October.
On that front, there may be some good news, with Cooper hopeful of having Cane fit to start against the Reds.
However, the reinforcements may come too late for the Chiefs, who are bottom of the New Zealand conference with three wins, a draw and six losses after suffering a 47-19 hiding by the Wellington Hurricanes over the weekend.
Cooper's side are 22 points behind the conference-leading Canterbury Crusaders, with seven rounds of the regular season left before the playoffs.
Cooper said the injuries had given chances for younger players to develop but suggested more pain was in store.
"While they're learning, I think the Chiefs are going to have to hurt a bit there."
(Reporting by Ian Ransom in Melbourne; Editing by Greg Stutchbury)
