Parker has been called up every month except June this season. In 10 games, he has given up nine earned runs on 14 hits and four walks over 13 1/3 innings.
Manager Rick Renteria would not say who specifically will be added on Tuesday.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.