Customers who buy their homes through Sears, Roebuck & Co. financial centers will be able to carpet and furnish them with Sears products--at a discount.

Sears, the nation's largest retailer, last year began to pioneer what has been called the financial supermarket. At the company's annual meeting yesterday, Sears Chairman Edward R. Telling said that the Chicago-based giant will try to mesh its financial services with its retail services.

Telling also said that Sears--which owns a savings and loan association in California, as well as a major securities firm, a real estate broker and an insurance company--is looking to buy institutions in other states to build a deposit base for its so-called financial network. He said Sears wants to offer automatic teller machine services at its stores and electronic home banking to its customers.

Telling only sketched the company's plans to shareholders, meeting in Greensboro, S.C. He said that the program to grant discounts on carpeting, appliances and furniture to those who buy homes through Coldwell Banker, the Sears real estate brokerage subsidiary, would begin later this month.

He said the Sears financial network, which also includes Allstate Insurance and Dean Witter Reynolds, plans to:

* Begin offering a new family of tax-exempt investment trusts.

* Become the first private distributor of securities that are backed by home mortgages.

* Test a plan in California through which homeowners will have a line of credit that is based on the equity they have in their houses. Their equity is the difference between what they owe on their mortgages and the market value of the dwelling. The homeowners can tap the line of credit by check. Merrill Lynch & Co., the nation's biggest broker, introduced a similar plan two years ago.