Schoeneweis was acquired from the Mets in a deal last December and compiled a 7.12 ERA in a season that was marred by personal tragedy for the left-hander.
Schoeneweis' wife, Gabrielle, was found dead in the couple's home in May, and he twice left the team, once going on the bereavement list following her death and another time when he went on the disabled list with depression.
The D-backs have several other left-handed relief options, so it seems unlikely they will re-sign Schoeneweis.
Infielder Chad Tracy and pitcher Doug Davis filed for free agency Thursday, the first day that players were allowed to do so. Right-hander Daniel Cabrera was outrighted to Triple-A Reno on Thursday and opted instead for free agency. None of the three are expected to return.
Those are the only D-backs players eligible for free agency, though outfielder Alex Romero could opt for free agency rather than accept an outright assignment to Reno.
The D-backs have 15 days of exclusive negotiating rights with their free agents.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.