Manager Joe Girardi said that Soriano threw on Tuesday and seemed better than the last time he played catch, but the Yankees still weren't convinced Soriano was ready for the next steps.
"If we felt it was 100 percent, we would have continued with this throwing program," Girardi said. "He's close, but he's not quite there."
Sidelined since May 14 with right elbow inflammation, Soriano was transferred to the 60-day disabled list on Wednesday to create room for right-hander Cory Wade on the active roster.
He signed a three-year, $35 million deal with New York after leading the American League with 45 saves for the Tampa Bay Rays last year.
Additionally, right-hander Joba Chamberlain was seen by Dr. James Andrews in Pensacola, Fla., on Wednesday and will undergo season-ending Tommy John surgery on Thursday.