WASHINGTON — Senator Elizabeth Warren plans to introduce a bill in coming weeks that would intensify the scrutiny of bank mergers, a signal less of legislative action to come than of her intentions for the finance industry if she is elected president.

The bill, a companion of which will be introduced Wednesday in the House by Representative Jesús “Chuy” García, Democrat of Illinois, will almost certainly go nowhere in the Republican-controlled Senate. But its argument that the “review process for bank mergers is fundamentally broken” indicates that Ms. Warren, Democrat of Massachusetts, still has the financial industry in her sights.

It would demand more extensive testing for vulnerabilities when two banks want to merge, a bid to slow financial sector consolidation and lean against the formation of huge banks. And it would require the Consumer Financial Protection Bureau, which Ms. Warren helped create, to approve any merger in which one of the banks offers consumer financial products.

The proposal is the latest sign that if Ms. Warren wins the White House, her victory could usher in a new era for the rules that govern banking. Financial regulators, including the Federal Reserve, have been relaxing requirements put in place after the 2008 financial crisis in recent years, often at the behest of Congress. The changes have jibed with the Trump administration’s broader push for a lighter-touch government.