Davis is under contract with the Pelicans for two more seasons.
However, the 25-year-old has a player option in his current deal, meaning he can become a free agent in 2020.
And Davis, who will earn $25.4 million this season, already has a shortlist of teams he could join if he quits New Orleans.
Sheridan of GetMoreSports says the Boston Celtics, Los Angeles Lakers, New York Knicks, Philadelphia 76ers and the Pelicans are the five teams Davis will consider.
It’s claimed that a key factor will be how successful the Pelicans are in the first half of the 2018-19 season.
If New Orleans are struggling or have an average start to the campaign, it’s unlikely that Davis will be traded before the deadline.
“Winning and being the best player on the floor every night” matter most to Davis, a source told GetMoreSports.
GetMoreSports add that Boston are leading the race to sign Davis, with the Lakers next in line.
The power forward averaged 28 points, 11 rebounds and two assists per game for New Orleans last season.
Davis guided the Pelicans to the Western Conference semi-finals last time out, with New Orleans losing 4-1 to the eventual champions Golden State Warriors.
NBA pundit Stephen A. Smith recently claimed Davis no longer wants to play for the Pelicans, adding the Warriors could land the big man.
“I definitely think that he wants out,” Smith said.
“He signed with Klutch Sports. Anthony Davis doesn’t want to be in New Orleans any longer.
“Whether it’s definitively the Los Angeles Lakers, I’m not so sure.
“I would keep Golden State and Boston in the mix because Golden State doesn’t know what Kevin Durant is going to want to do.
“And Boston obviously has the requisite pieces to put together to make sure they can get a player the quality of Anthony Davis.”
Davis and the Pelicans kick off their NBA season against the Houston Rockets on October 18.