The duo has until May 24 to remove their names from consideration.
Teammate Joel Berry, meanwhile, also initially declared for the draft but said on Tuesday he would withdraw his name from the draft and return to Chapel Hill for his senior season.
Berry averaged 14.7 points per game and earned Final Four Most Outstanding Player honors after leading the Tar Heels to the national title game win over Gonzaga. The junior had 22 points and six assists in the championship game.
Hampered by a foot injury for part of the season, Pinson averaged 6.1 points, 4.7 rebounds and 3.7 assists per game while Bradley, a freshman, averaged 7.1 points and finished second on the team in rebounding.
Justin Jackson, who tested the draft waters a year ago, already has signed with an agent.
Should Pinson and Bradley also elect to return, coach Roy Williams would have a formidable lineup to defend the Tar Heels' national championship.