According to ESPN.com's Jonathan Givony, Carter "is a favorite of the Memphis front office and especially the coaching staff."
Givony added that the Grizzlies, who have seen interest in the No. 4 pick from at least seven teams, "hope to move back a few spots" if they are able to strike a deal Thursday night at the Barclays Center in Brooklyn, New York.
Carter wasn't the headliner in Duke's frontcourt last season—that distinction belongs to Marvin Bagley III—but he established himself as a surefire lottery pick thanks to his versatile offensive repertoire.
As a freshman, Carter averaged 13.5 points, 9.1 rebounds and 2.1 blocks per game on 56.1 percent shooting from the field. He also shot 41.3 percent on 46 three-point attempts.
The Grizzlies, who have been mentioned frequently in trade rumors leading up to the draft, are looking to package the No. 4 overall pick with Chandler Parsons' contract, according to The Athletic's Michael Scotto.
Parsons, 29, is owed $49.2 million guaranteed over the next two seasons and has a history of chronic knee injuries that has limited him to 70 appearances since he signed with the Grizzlies in 2016.