Davis, who requested a trade in January, and Griffin, who was hired in April, are expected to continue a dialogue in the near future, sources said.
Additional conversations about Davis' future may be largely focused between Griffin and Davis' agent, Rich Paul, who also attended Wednesday's meeting, sources said.
Davis, 26, can become a free agent next summer, but Griffin has been determined on selling him on the Pelicans through a new prism. New Orleans plans to draft Duke's Zion Williamson with the No. 1 overall pick, and Griffin has made strides with hires in his front office, medical and training staff and practice facility improvements.
Davis is eligible to sign a five-year, $235.5 million supermax contract extension on July 1.
New Orleans could have eager trade suitors -- the Los Angeles Lakers and Clippers, Boston Celtics and New York Knicks -- should Griffin engage in trade talks, but so far that hasn't happened, sources said. Griffin has been determined to make a case for Davis to stay.
Davis made his trade request after the Pelicans fell out of the playoff chase. He was the No. 1 overall pick in the 2012 NBA draft. He's a six-time All-Star and a three-time first-team All-NBA selection.