In Tuesday's Game 5, Bryant scored a team-high 19 points in 29 minutes, despite lingering soreness and swelling in his sprained left ankle.
Jackson said that he wouldn't be afraid to play Bryant heavy minutes in Thursday's potential close-out game.
"This is a game we'll go all out to win and if it's 40 minutes we'll do it," Jackson said. "We're certainly not out of the woods on this situation, just because he had to play the day after, or two days after he sprained his ankle.
"It's still a lot of things going on. So we just have to wait and hope for each game that we get, and go through this series in the best possible shape we can get in at this point. There's nothing we can do about it but just play with it."
Bryant spent Wednesday morning rehabilitating his ankle with the Lakers medical staff instead of taking part in a light workout at the team's practice facility before the team boarded a charter flight to New Orleans.
"He's sore, obviously," Jackson said. "We're trying to keep the swelling down again. We're going through that whole process that he started on Sunday [after spraining the ankle in Game 4] to try and eliminate the swelling and try and get some of the soreness out of that joint."
Bryant was unavailable for comment Wednesday.
Asked whether he thought Bryant would play on Thursday, teammate Pau Gasol laughed and said, "I think so. What do you think?"
Ramona Shelburne is a reporter and columnist for ESPNLosAngeles.com.