Minnesota president Gersson Rosas had been trying to move up to No. 4 or 5 before finally getting No. 6, sources said.
ESPN projects Texas Tech shooting guard Jarrett Culver as the No. 6 prospect in the draft.
The Suns had the best chance at the top pick in the draft heading into the lottery before falling to sixth.
Saric averaged 10.5 points and 5.5 rebounds per game last season, his third in the league and first with Minnesota after being drafted by Philadelphia.