Kasten also said his fear is "not based on medical evidence," even though as CEO he has access to all medical information the club has on each of its players.
Kasten's comment came less than a week after the club gave reporters a vague description of "elbow inflammation" as the reason for Billingsley's placement on the disabled list Saturday after he underwent an MRI.
The club also said Billingsley would have a second MRI when the inflammation subsides later this week to determine the full extent of the injury.
Billingsley was placed on the disabled list on Saturday, the same day the Dodgers acquired starting pitcher Josh Beckett in the nine-player blockbuster trade with Boston.
Billingsley spent two weeks on the disabled list in July with what also was listed as elbow inflammation, although Billingsley at the time said he was fine and he continued to throw. This time he has been shut down, while speculation has heated up that the Dodgers are looking to acquire yet another starting pitcher by Friday night's deadline to add players for the postseason.
However, the club is now believed to have shifted its targets to relievers after the double loss Wednesday of closer Kenley Jansen to an irregular heartbeat and Scott Elbert to elbow pain that is expected to require off-season surgery.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.