That’s according to Sporting News’ Sean Deveney, who claims the Celtics will not be letting any of their 2019 draft picks go before the February 7 trade deadline.
Boston have endured a difficult campaign so far, currently lying fifth in the Eastern Conference standings.
But it has been the troubling performances of late which have raised some concern over their current roster.
In last week’s loss to the Orlando Magic, Kyrie Irving could be seen frantically waving his arms at his team-mates after Jayson Tatum missed a mid-range jumper to tie the game.
Irving has called out the young core on multiple occasions this season and there has already been a number of team meetings behind closed doors to try and rectify any issues.
Their disappointing form this campaign has led to suggestions that Boston may look to make a trade at the deadline to improve their roster.
They have three first-round draft picks this year which could be used in any potential deals.
But Deveney reports Boston want to hold on to all three so they can try and go for Davis ahead of draft night.
Boston will likely face competition from the Los Angeles Lakers for a Davis trade.
The Lakers also have a number of assets available to them, but it could all come down to whether or not Davis informs the New Orleans Pelicans of one particular team he prefers.
The 25-year-old will become a free agent in 2020, meaning the team that trades for him risk losing all their assets for a player that could walk in a year.
And Fox Sports analyst Chris Broussard believes it will be the Lakers who ultimately win the race for Davis.
“This summer New Orleans is going to offer Anthony the supermax contract, and he’s going to reject it,” he said earlier this month.
“They’re going to realise that he’s not staying, if he’s not taking the supermax then we’re going to have to trade him.
“Anthony’s not going to be the bad guy. His agent Rich Paul, also LeBron’s agent, will talk to New Orleans and be like ‘he’s not going to stay long-term, he’s given it seven years and you haven’t won, he wants to win’.
“Okay, where does he want to be traded? The Lakers.”