That is the claim made by Fox Sports’ NBA expert Colin Cowherd.
Davis is wanted by both franchises, but is still under contract until 2020.
And this summer, he can sign a supermax contract at the New Orleans Pelicans, which would extend his stay by four years.
However, if he rejects the supermax deal, it will be the biggest indication yet that he will leave.
It is reported the Los Angeles Lakers will have to give up two young prospects as well as draft picks to land Davis.
Lonzo Ball and Brandon Ingram were rumoured to be players the Lakers would use, however that could all change now.
Ball suffered an injury on Saturday and will be out until after February’s All-Star break, while Ingram has failed to deliver any spells of solid performances.
And Cowherd hinted that this could lead to Davis heading to the Boston Celtics instead, who would likely give up a deal involving one of or both of Jayson Tatum and Gordon Hayward.
“Anthony Davis is in a losing franchise, but he’s a great player, we all know that,” Cowherd said.
“Davis is represented by Klutch Sports, which represents LeBron.
“In order to get him, rather than wait a year and a half, the Lakers will need to trade for him. The Celtics are also interested.
“And the Celtics have a lot of parts.
“When the season started, Lonzo Ball and Brandon Ingram were real assets.
“Ingram has been one of the biggest disappointments, and Lonzo Ball, you have to say it, he’s injury prone.
“So you have two assets that now, New Orleans won’t want. Boston still has two assets.”