The 25-year-old is under contract with the Pelicans for two more years.
However, Davis has a player option in his current deal, letting him test free agency in 2020.
Davis has been linked with the Boston Celtics and the Los Angeles Lakers in recent weeks.
However, Pelicans head coach Gentry says New Orleans will not trade their star for anyone – not even Beyonce.
“When you have someone who you can trade for anyone, I think that makes him the best. Or at least most valuable,” Gentry said.
“Now, we aren’t considering that.
“We wouldn’t trade him for anyone. Even Beyonce.
“I think that makes him untouchable.”
Davis, who will earn $25.4 million this season, averaged 28 points, 11 rebounds and two assists per game for New Orleans last time out.
The power forward 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 analyst Stephen A. Smith recently claimed Davis no longer wants to play for the Pelicans.
“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 Thursday night.