Upon first becoming a tropical cyclone, the depression was located within an area of weak steering currents. Initially it was forecast to remain offshore; with warm waters and light wind shear, the depression was forecast to intensify into a strong tropical storm, and possibly attain hurricane status. However, the circulation was difficult to locate, and as such its exact motion was uncertain. Ships in the region confirmed the center of the storm as further northeast than previously thought, but also confirmed tropical storm force winds; as a result, the National Hurricane Center upgraded the depression to Tropical Storm Norman. Strengthening continued, and Norman attained peak winds of , shortly prior to making landfall west of Lázaro Cárdenas, Michoacán, late on September 20.
