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"Anthony wants to be traded to a team that allows him a chance to win consistently and compete for a championship," ESPN reported Davis' agent Rich Paul as saying.
"Anthony wanted to be honest and clear with his intentions and that's the reason for informing them of this decision now. That's in the best interests of both Anthony's and the organisation's future."
The NBA trade deadline is February 7, but New Orleans has given no indication it wants to trade him this season.
The Pelicans selected Davis with the No 1 overall pick of the 2012 NBA Draft. He has been named first-team All-NBA three times and has appeared in five All-Star games. He turns 26 in March.
Davis signed a five-year, $US127 million contract before the 2016-17 season. The fifth year is a player option, so Davis could become a free agent in the summer of 2020. He would be eligible to sign a five-year, $240 million supermax extension this summer.
The Los Angeles Lakers and Boston Celtics have been mentioned often as the teams that will pursue Davis most aggressively. LeBron James also is represented by Paul, and in December, James was asked his thoughts about the possibility of Davis one day joining him with the Lakers.
"That would be amazing," he said.
The Lakers are in a position to try to put together a package now to appeal to the Pelicans. The Celtics cannot trade for Davis under league rules until July 1 because Davis and Kyrie Irving couldn't be on the same roster because of designated rookie exceptions in their contracts.
The New York Knicks might be in play, too.
"You're gonna see the Knicks try to be aggressive here now," ESPN's Adrian Wojnarowski said on Golic and Wingo.
"If you're the Knicks, Kristaps Porzingis is a player who New Orleans would have to believe they could re-sign if they traded for him. And he may not be open to that. So, if you're the Knicks, the best chance you have is getting the No 1 overall pick and being in a position post-lottery time where you could tell the Pelicans, 'Hey, you can have Zion Williamson, you could rebuild with him.'"
Davis is averaging 29.3 points and 13.3 rebounds per game. He has missed the past four games with a fractured left index finger.
At 22-28, the Pelicans are in 13th place in the Western Conference, six games out of the final playoff spot.