The Trump administration is poised to roll out a plan for trading digital versions of securities that could reshape the landscape of the American stock market as it continues to loosen the rules for free-wheeling crypto markets.

The Securities and Exchange Commission is expected to release its so-called innovation exemption for tokenized stocks as soon as this week, creating a new framework for betting on the fortunes of publicly traded companies, according to people familiar with the matter.

In a surprise move, the SEC is leaning toward a decision to allow the trading of tokens that do not have the …