"Sam's going really well and could be (back) this week or next week," Cooper told reporters on Tuesday.
Cane was invited to a one-day All Blacks camp last month, boosting his chances of making the defending champions' squad for the World Cup in Japan, which starts in September.
Chiefs are currently 12th in the overall Super Rugby standings, two points above the Blues who have played a game less.
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(Reporting by Rohith Nair in Bengaluru; Editing by Simon Jennings)
