The Lakers are one of four Davis reportedly informed the Pelicans he would like to be traded to.
The Clippers and Bucks are the other teams Davis would consider signing with long term, according to the Athletic.
The Pelicans are 23-31 and 2-8 in their last 10 games.
As Thursday's 3 p.m. ET trade deadline approaches, reports and rumors continue to trickle out. That said, many around the league seem to believe the Lakers' offer is the best the Pelicans can expect to receive.
The Celtics can't trade for Davis this season while star point guard Kyrie Irving is on the roster because of the "Rose Rule".
Clearly, the Lakers are a buyer - or at least will be by summer, if they're not yet - and the Pelicans are a seller.
Still, Davis' camp has been engaged in an aggressive campaign to push back on the possibility of the All-Star center's future in Boston, encouraging the Pelicans to do a deal with the Lakers or another preferred team prior to Boston's chance to become active in deal talks in the offseason.
In this draft especially, the difference between first and second is a massive gulf. The Pelicans could wait until the draft lottery in May, when they'll have a better idea of when and how Boston's protected picks in deals with Philadelphia, Memphis and the Clippers could be conveyed in a deal.
The latest offer, which included six players and two first round picks, was rejected by the Pelicans, as they wanted four first-round picks. It was recently suggested the Davis saga was weighing heavily on the Lakers young core, as they've been connected to a possible deal.
"Another guy who can knock down threes would make them even more unsafe".
One week ago, Davis requested to be traded from the Pelicans. But even that would be hard, meaning LA's best chance to land him would be ahead of Thursday's deadline. He reportedly would sign an extension with any of those teams.