The incumbent often prefers to go last in trying to convince a player to stay with the team.
Leonard is expected to decline his player option and become an unrestricted free agent.
He was named NBA Finals MVP after helping the Raptors win the franchise's first championship in his first season with the team. He was acquired in a blockbuster trade with the San Antonio Spurs last summer.
Raptors president Masai Ujiri said earlier this week that he texted with Leonard as recently as Monday and talked to Leonard's uncle and adviser, Dennis Robertson, on Tuesday. Ujiri said he's "confident" Leonard will decide to return to Toronto.
"We'll wait. He's our player and he's a superstar on our team and we'll wait on that," Ujiri said.