The Reagan administration has proposed legislation that would substantially broaden the ability of bank companies to enter the insurance, stock brokerage and real estate businesses.

The bill, sent to Congress early this summer, would set up new rules to make sure that the banks--as well as their customers--are protected if their parent companies should venture into new, riskier fields.

But the Federal Deposit Insurance Corp. is worried that Congress will not take any action and that banks will get into many of those activities without proper supervision because states are rapidly rewriting their own regulations.

As a result, the FDIC is considering a major step: writing its own regulations restricting other business activities of all banks that have FDIC insurance.

Although the FDIC is responsible for insuring deposits at nearly all the nation's 15,000 banks, it is one of three federal agencies that regulate and examine banks. It is the primary federal regulator for the 9,300 state-chartered banks that are not members of the Federal Reserve System. The Comptroller of the Currency regulates federally chartered banks, while the Federal Reserve system regulates state banks that choose to join the Fed.

But the FDIC is considering imposing the rules on all three kinds of banks, citing its responsibility to protect the $14 billion insurance fund, which is tapped to pay off depositors in the event of a bank failure and to assist a healthy bank that takes over a failing bank.

FDIC officials said that it would be the first time the agency cited that responsibility as a reason not only to intrude on its fellow federal bank regulators, but to take steps to limit state regulators.

It is unlikely that the FDIC would face serious opposition from either the Fed or the comptroller. Federal Reserve Board officials, including Chairman Paul A. Volcker, are more worried about bank expansion into new, riskier fields than are either the FDIC or the comptroller. Comptroller of the Currency C.T. Conover is on the FDIC board and joined in the unanimous vote last week to move forward on the rules.

If the FDIC puts the rules in place, presumably the only way a bank could free itself from the regulations would be by giving up deposit insurance, a move that surely would send most of its depositors looking for a new bank.

The FDIC is seeking comments on whether it should proceed to regulate "the direct or indirect involvement of insured banks in real estate or insurance brokerage and underwriting, data processing services, travel agency activities and other financially related activities."

It also wants comments on what limitations, if any, the FDIC should impose on the ownership of insured banks by companies engaged in these non-banking activities.

FDIC Chairman William Isaac said that if Congress passes the administration bill--which would force bank companies to set up separate subsidiaries to engage in these activities and insulate the bank from any losses the subsidiaries might incur--the FDIC would not have to take any action.

But, he said, "Congress is immobilized and can't come to grips with these issues, and a number of states are taking the lead." In an attempt to attract new business, some states, such as North Dakota, are preparing to allow banks to engage in insurance and other activities.

Isaac said the agency has not decided to go ahead and write the regulations. "We are genuinely seeking intelligent input," he said. But another FDIC official said it should be clear that the agency would not take the step of asking for comments on a possible course of action if it were not predisposed to act.