Forward Chris Brown was assigned to Portland in a corresponding move.
Once one of Phoenix's top blue liners, Klesla was waived Tuesday after struggling to start the season. No team claimed the 31-year-old and he was assigned to Portland, but did not play for the Pirates.
Klesla missed the first three games of the season because of a preseason concussion. He had a goal and two assists in 15 games.
He appeared in 65 games in 2011-12, when the Coyotes reached the Western Conference finals for the first time. He played 38 games during the lockout-shortened 2012-13 season, scoring two goals with six assists.