"Win championships or nothing. To lead this franchise, you've got to be that way," the Lakers star said Tuesday before L.A. played the Detroit Pistons at Staples Center.
Bryant, who was making his first public comments to local media since suffering a season-ending shoulder injury on Jan. 21, added that it's easy to recognize that identity in players.
"You can tell," he said. "It almost makes no sense to think that way, so when a person says that, you're kind of like, 'You're weird.' That's probably the guy."
Would it be difficult for the next player who succeeds Bryant to carry on his mentality?
"It won't be difficult if they have it," Bryant said. "They'll look at you like it's a silly question that you even asked them. Look, there's different ways to skin a cat. They won't probably be as sarcastic as me or something like that. Magic [Johnson] was the same way, but he smiled a lot and was much, much nicer to [the media] than I was. There's different ways to go about it."
Bryant was asked if he's comfortable leaving the Lakers if the franchise doesn't have someone like that in place.
"No, I'd much rather hand the keys over to somebody and let them take this organization right from the jump," he said. "I'd much rather do that. Hopefully we can. But if not, even when I'm retired, that's one of the things that I'll be hell-bent on -- to make sure this franchise gets back to where it needs to be."
In the meantime, he'll be working on rehabbing his shoulder, his third consecutive season-ending injury, as he works to return in 2015-16, his 20th and likely final NBA season.
"It's discouraging," he said. "You have an injury, you have another one, then you have another one. It's discouraging. But, I respond to it the same way I always have -- just stick to the process."
Bryant admitted the difficultly of going through that process again knowing he could be hurt just as quickly.
"That's very difficult," he said. "You start trying to gauge the importance of a Monday workout or a Wednesday workout. Like, 'How really important is it?' because I can do all this stuff, and then next year in one minute it's all gone. Those are the challenges that I have to struggle with mentally and just try not to overthink that. Just go out there and just do it. Every single day just do it and control what you can control."