Per Wojnarowski, Aldrich will become an unrestricted free agent after the T'Wolves declined to guarantee his $6.9 million contract.
The 29-year-old spent two years in Minnesota and played sparingly during the 2017-18 season.
He appeared in 21 games, averaging 0.6 points and 0.7 rebounds in 2.3 minutes per contest.
He was traded to the Oklahoma City Thunder that night and went on to play two seasons with OKC.
Aldrich has 23 career starts to his credit, as he has primarily been a reserve big man during his time in the NBA.
His most productive season came in 2014-15 with the Knicks when he put up 5.5 points, 5.5 rebounds and 1.1 blocks per game.
Minnesota's frontcourt rotation won't change much with Aldrich gone, as Karl-Anthony Towns, Gorgui Dieng and Taj Gibson will continue to play the bulk of the minutes, barring additions via trade or free agency.