The Securities and Exchange Commission’s expected changes to U.S. stock-trading rules are likely to prompt fierce opposition from the brokerages and electronic market-making firms that handle small investors’ orders, analysts and traders say.

The agency is preparing to propose major changes to the stock market’s plumbing as soon as this fall, The Wall Street Journal reported Monday. SEC Chairman Gary Gensler is expected to outline some of the SEC’s plans Wednesday in a speech. The changes grew out of the frenzied trading in GameStop Corp. and other meme stocks in early 2021, which resulted in heavy scrutiny of the handling of individual investors’ trades.

One of the most consequential changes being discussed by the SEC is a possible requirement to send more individual investors’ stock orders to auctions, where trading firms could compete to fill the order at the best price, the Journal reported.

Such auctions would represent a big shift to the working of the U.S. stock market. Currently, when investors enter orders using brokerages such as Robinhood Markets Inc. , the brokers often route the orders to electronic market-making firms that execute them. In return, the market makers frequently pay the brokerages cash incentives, a practice called payment for order flow.

Mr. Gensler has criticized such payments as being a conflict of interest for brokers, and he has suggested that the business of retail market-making is too concentrated. Market makers are firms that buy and sell stocks throughout the day and make a profit from collecting a difference between the buying and selling price. A handful of such firms, including Citadel Securities and Virtu Financial Inc. , handle the lion’s share of U.S. stock trades for individual investors.

By funneling more such trades into competitive auctions, the SEC would seek to have more market makers competing for individual investors’ business, in hopes that investors get better prices for their orders.

Retail brokers and market-makers entrenched in the current system will fight Mr. Gensler’s changes, potentially even filing lawsuits to block any regulatory changes, said Joe Saluzzi, partner and co-founder of brokerage Themis Trading LLC.

“Any time you threaten an existing status quo that benefits a lot of people, they will fight you tooth and nail,” said Mr. Saluzzi, whose firm handles stock trades for institutional investors and hedge funds.

A spokeswoman for the SEC declined to comment.

Executives at retail brokerages and market-making firms have been wary of Mr. Gensler’s plans since he indicated last year that he would pursue a shake-up of market structure. Firms such as Robinhood, Virtu and Citadel Securities say investors get high-quality executions from the current system, because the market-makers that handle small investors’ trades provide better prices than they would get if their orders were routed to public stock exchanges. Payment for order flow has also made it possible for brokerages to offer zero-commission trading. 

Virtu has estimated that U.S. individual investors saved $11 billion on their trades in 2020 by having those trades routed to market makers instead of exchanges.

Virtu criticized Mr. Gensler’s idea of bringing order-by-order competition for individual investors’ stock orders, saying it would eliminate a big benefit of the current system: the guarantee that a market maker must fill every retail order it gets from a broker at a price at or better than the best price available on public stock exchanges.

If those orders were routed to auctions instead, the retail brokerage wouldn’t have a clear way to ensure that they would be executed. If an order went unexecuted in an auction, the retail brokerage would need to find another place to execute and bear additional costs, such as exchange transaction fees. The end result wouldn’t necessarily be an improvement for ordinary investors, according to Virtu.

Virtu Chief Executive Douglas Cifu suggested in an emailed statement that the SEC would face litigation if it pushed through with the changes reported by the Journal.

“The entire market will be evaluating any proposal to ensure it complies with the rule-making requirements, aligns with the SEC’s mandate, and includes complete economic and competitive analysis,” he said.

Robinhood declined to comment. A spokesman for Citadel Securities said the firm looks forward to reviewing the SEC’s proposals and working with the agency. “It is important to recognize that the current market structure has resulted in tighter spreads, greater transparency, and meaningfully reduced costs for retail investors,” he said.

One group that may be happy with Mr. Gensler’s proposals is stock exchanges, which would be likely to win more orders from individual investors that are now executed privately by market makers, said Hitesh Mittal, founder and CEO of trading-technology firm BestEx Research.

“Exchanges are going to love it,” Mr. Mittal said.

Write to Alexander Osipovich at alexander.osipovich@wsj.com