The 37-year-old Valverde was packing up his belongings Thursday morning and said he would return to his native Dominican Republic. The three-time All-Star is hopeful he'll get an offer from another team soon.
A non-roster invite, he posted a 4.15 ERA with eight strikeouts and one walk in nine spring appearances with San Diego.
Valverde had been out of baseball since being released by the New York Mets last May. He had a 5.66 ERA.
Valverde has 288 career saves.