Jeffress will likely be designated for assignment prior to his release, Rosenthal reports.
After playing an integral role in Milwaukee's bullpen last season, the right-hander has authored a 5.02 ERA and 3.97 FIP with three blown saves over 52 innings.
Jeffress has been on the 10-day injured list with a strained left hip since Aug. 26.
The Brewers are in the midst of a playoff hunt that is looking increasingly bleak. Currently 6 1/2 games back of the division-leading St. Louis Cardinals, the NL Central crown is distant. Milwaukee is also four back of the second-place Chicago Cubs, who currently own the second NL wild-card spot.