Rozee sprained an ankle in Saturday's win against North Melbourne, which was his return game after missing two matches because of a hamstring strain.
Hinkley says Rozee's status for Thursday night's Adelaide Oval clash against the Blues remains unclear.
"Clearly it's a short turnaround, five days," Hinkley told reporters on Tuesday.
"And we'll give it to the very last minute to figure out where he's at, but if there's any danger we won't play him.
"This is not soft tissue so it's a more manageable injury, which is something there will be a little bit more pain than danger of hurting it again.
"And we go in to the bye the week after, there's plenty of time to recover and rest after that, so we'll be bullish right to the moment probably.
"It's more about dealing with the pain of a sore ankle ... they can be sore but you can actually get through."
Goalsneak Willie Rioli (calf) is sidelined but key forward Charlie Dixon will return after being rested for the game against the Kangaroos.
The Power (eight wins, three losses) hold third spot on the ladder entering the fixture against the eighth-placed Blues (seven wins, four losses).
Hinkley said the presence of Carlton's attacking "twin towers" Charlie Curnow and Harry McKay was the exact reason why Port bolstered their defence in the off-season.
The Power recruited tall backmen Esava Ratugolea from Geelong and Brandon Zerk-Thatcher from Essendon to help counter opponents like Curnow and McKay.
Harry McKay runs to embrace fellow Blues forward Charlie Curnow after a goal against the Crows. (Joel Carrett/AAP PHOTOS)
"There's no doubt about that," Hinkley said.
"When you come up against the size of those two boys and the talent that they have, that's certainly the reason we went looking last year to find some players to help us in that area."
Ratugolea last-start kept North Melbourne's Nick Larkey goal-less, ending the Kangaroos attacker's streak of kicking a major in 29 consecutive games.
"(Defensively) we're going OK - win-loss record would suggest we're doing OK in most phases of the game," Hinkley said.
"We haven't always been perfect, we've had some challenges at different times, whether it be defence or offence.
"You can only go by where you sit currently and for us right now, we've put a good body of work together that puts us in a healthy position.
"But it's a close competition, you don't need to slip."
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