The Lakers heard Cuban's advice and didn't appreciate it.
"We're aware of Mark Cuban's comments and feel they are inappropriate," Lakers spokesman John Black said in a statement. "As to the issue itself, we will not comment publicly on the amnesty issue as it relates to any of our players."
The Lakers will not file a formal complaint to the NBA about Cuban's comments, but the league could choose to fine the Mavs' owner after reviewing the interview.
Bryant had little reaction when asked about it before Friday night's game against the Portland Trail Blazers.
"I'll bet he did," Bryant said with a chuckle when asked if he'd heard what Cuban said.
Cuban got himself into some hot water during an appearance on ESPN Dallas 103.3 FM's "Ben and Skin Show" when the topic of the Lakers came up.
"If you look at their payroll, even if Dwight (Howard) comes back, you've got to ask the question: Should they amnesty Kobe?" Cuban said. "You just don't know, right? It's the same reason I wouldn't get rid of Dirk (Nowitzki). I'll take a hit for a season rather than get rid of Dirk. That's just it. I've made that commitment to him over the years, and he's returned that commitment. Maybe that's selfish, but that's just the way it is.
"So I'm just saying that hypothetically. When I say amnesty Kobe, I don't think they'd do it, but they've got some choices to make. Now, they're in a big market, but they're still limited. The Knicks, the same thing. Boston, same thing."
Bryant is on the books for a league-high $30.45 million salary next season, the last year of his contract.
The Lakers' payroll is slightly more than $100 million this season and will probably be in that same range next season if Howard re-signs in the offseason.
This is the last season of a dollar-for-dollar penalty for teams over the luxury tax limit ($70.307 million this season). Beginning next season, the luxury tax starts at $1.50 per dollar and escalates for every $5 million a team is over.
If the Lakers are $30 million over, their luxury tax bill would be a whopping $85 million next season.
If L.A. trims the payroll down to $20 million over the tax, the Lakers still would get hit with a $45 million bill. And they'd be subject to the even heavier repeater rate in 2014-15, although Steve Nash's $9.7 million salary is the only contract on the Lakers' books for that year right now.
Next season is the Lakers' last chance to amnesty a player, and Bryant is one of four players the Lakers can do it to. The others are Pau Gasol, Metta World Peace and Steve Blake. If the Lakers waive any one of those players this summer, they would not have to pay luxury taxes on their salaries, but they would still have to pay that player's salary.
The Lakers will play the Mavericks in Dallas on Sunday.
Information from ESPNDallas.com's Tim MacMahon was used in this report.