WASHINGTON (AP) _ Sears, Roebuck and Co.'s financial arm, Dean Witter, Discover & Co., sought federal clearance Tuesday to offer 29.5 million shares of common stock to the investing public.

The stock offering, which had been expected, is the prelude to Sears' planned spinoff of the New York-based brokerage, money manager and credit card unit. Sears is jettisoning its financial businesses except for its Allstate insurance unit in an effort to shore up its sagging retailing business.

Documents filed with the Securities and Exchange Commission said the Dean Witter stock offering would be used to repay Dean Witter's indebtedness to Sears.

Sears said it will still own more than 82 percent of Dean Witter's common shares after the stock offering.

However, the Chicago-based conglomerate said it plans to spin off Dean Witter by Dec. 31, 1993 by means of a special dividend paid to Sears stockholders out of its holdings in the financial firm. The company will also divest its Coldwell Bankers real estate subsidiary.

Dean Witter includes the Dean Witter Reynolds brokerage nand the Discover credit card business.

A published report Tuesday, which company officials declined to confirm or deny, said Sears plans to close up to 100 of its smaller stores, eliminating as many as 5,000 jobs,