Thompson, who will enter free agency this summer, is earning $18.5 million this season - the last of a five-year, $82-million contract he signed with the Cavaliers in 2015.
Drummond's surprise addition could create a logjam in Cleveland's frontcourt. Thompson has started all 48 of his games this season at center for Cleveland, which also boasts Kevin Love and Larry Nance Jr. at power forward.
Thompson, 28, is averaging 11.9 points and 10.4 rebounds - both career highs. However, the Cavaliers have faltered to a 13-39 record and currently sit last in the Eastern Conference under first-year NBA head coach John Beilein.