Burke is the top-rated point guard in the draft whose advisors obviously don't think he's going to be available to Utah, which owns the 14th and 21st picks in the first round.
"I've been in communication with his people," Perrin said. "They've kind of drawn the line on how many workouts they are going to do. ... I don't think we'll get him in."
Burke is expected to be a top-eight pick in the draft. Lehigh's C.J. McCollum and Syracuse's Michael Carter-Williams are rated just behind Burke and aren't expected to be around when the Jazz pick.
Both players, however, have come to Utah for a workout.
Carter-Williams participated in Tuesday's workout. He averaged 11.9 points and 7.3 assists last season, but he shot only 29 percent from 3-point line.
"He sees the court and passes the ball well," Perrin said. "... We know it's a work in progress. For the most part, players in this draft have a few holes to work on. Michael's is shooting and getting a little stronger."
Carter-Williams, who stands 6-foot-5 and weighs 184 pounds, described his workout in Utah as "... tiring. The altitude is real up here. But it was good overall. I have fun. I think I did pretty well. I enjoyed it."
Carter-Williams probably won't be available when the Jazz pick in the first round, but he likely worked out for them because Utah won't have a point guard under contract after July 1.
If he slips to No. 14, the Jazz are intriguing to him.
"It would be a good spot for me to come in, play right away and chase some of my dreams." Carter-Williams said. "I think I could establish myself as a leader on the team. I wouldn't have [much] pressure because they don't have too many veterans. So it would be a great place for me."