The Lakers had agreed to send their entire young core of Lonzo Ball, Kyle Kuzma, Brandon Ingram, Josh Hart and Ivica Zubac to the Pelicans, as well as veteran guard Kentavious Caldwell-Pope, the people said.
In return, the Lakers would receive Davis and Solomon Hill - with the latter joining only for salary-cap relief.
"As a buyout candidate, perhaps the Lakers would make sense as a home for (Parker)", Bryan Kalbrosky of HoopsHype wrote.
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The Lakers clearly feel the Pelicans are asking for too much, while there's clearly enough people within the New Orleans organization who don't want to even think about moving Davis until after the season. There's a real possibility that the Pelicans and Davis could agree on a limited playing schedule post-trade deadline, but that's undetermined.
The NBA's trade deadline is Thursday at 3 p.m. ET.
Caldwell-Pope must approve any deal because he re-signed with the Lakers on a one-year, $12 million contract this summer after he played for the team in 2017-18.