Singler said the Blazers are the 10th team he's worked out for, with two more to go. The 6-foot-8 forward is expected by many to go late in the first round of next Thursday's draft.
"I just want to show them that I'm a competitor, I'm a winner," he said.
Singler played for South Medford High School before going off to Duke. He and Kevin Love, a star at Lake Oswego High School before playing for UCLA and the Minnesota Timberwolves, are among the most talented prep players to come out of Oregon.
As a result, Singler was met by a swarm of local reporters and television crews at his workout Thursday at the Blazers' Tualatin practice facility.
Singler said that when he hasn't been visiting teams, he's been training for the draft in Los Angeles, working on extending his range.
"I think today I shot the ball pretty well," he said.
He said he hasn't yet spoken to Love about the draft and what to expect.
"I'm sure eventually we'll get around to it," he said. "Kevin's a great resource."
Singler averaged 16.2 points, 6.9 rebounds and 2 assists per game during his four years under Mike Krzyzewski with the Blue Devils. He set school records with 147 starts and 4,887 minutes.
Singler averaged 20 points, 9 rebounds and 3.5 assists over the course of Duke's postseason march to the national championship in 2010. He was named the Final Four's Most Outstanding Player.
He surprised many when he stayed at Duke for his senior year.
Blazers coach Nate McMillan sees Singler playing primarily at the three spot.
"He's been winning since high school and all the way through college," McMillan said. "He's going to be a solid player."
The Blazers have the 21st and 51st picks in the upcoming draft.
Portland also worked out forward Jon Leuer out of Wisconsin, center Nikola Vucevic of USC and center Jeremy Tyler, who played last season with Tokyo Apache.
Tyler, who is 6-foot-10, is probably one of the more intriguing draft prospects because he left high school early to play overseas. He has impressed the teams he has worked out for, and as a result he's seen his draft stock rise.
"He is probably undervalued right now," said Chad Buchanan, Portland's acting general manager. "I think a lot of teams probably have interest in him."
Buchanan took over as acting GM after the Blazers abruptly fired Rich Cho last month.
He described the team as putting the "finishing touches" on their draft plan this week. He said the Blazers' two most pressing needs are probably at point guard and at center.
Portland has until June 29 to exercise a $7.8 million team option on Miller. If they don't, he will become a free agent.
Before he was let go, Cho said the Blazers would likely make the $8.8 million qualifying offer to keep Oden, who becomes a restricted free agent.
Oden didn't play this past season after microfracture surgery on his left knee. Because of various injuries, the No. 1 draft pick in 2007 has played in only 82 games over parts of two seasons, averaging 9.4 points and 7.3 rebounds.