Senate Banking Committee Chairman Christopher Dodd is considering scrapping the idea of creating a Consumer Financial Protection Agency, people familiar with the matter said, an initiative at the heart of the White House's proposal to revamp financial-sector regulations.

The Connecticut Democrat, who announced this month that he wouldn't run for re-election this year, has discussed the possibility of abandoning the push for a new agency during negotiations with key Senate Republicans as a way to secure a bipartisan deal on the legislation, these people said.

Mr. Dodd's offer is conditional, however: Republicans must agree to create a beefed-up consumer-protection division within another federal agency, these people said.

The apparent willingness to forgo an independent consumer-protection agency would be a major concession for Mr. Dodd, who had blasted the banking industry for lobbying aggressively to prevent the creation of such an entity. "The very people who created the damn mess are the ones now arguing that consumers ought not to be protected," he said in June.

Mr. Dodd's shift comes amid a new sense of urgency to enact revamped rules governing the financial sector in what is now a narrow window before the November election.