House Democrats, set to take over majority control next year, plan to probe President Trump’s involvement in hush payments arranged during the 2016 campaign to two women alleging affairs, according to a Democratic aide on the House Oversight Committee.

The aide said House Democrats have already begun probing the hush payments, including requesting records from the Trump Organization in September, and “plan to dig in deeper” by examining Mr. Trump’s role…

Rep. Jerry Nadler (D., N.Y.), who is a favorite to lead the House Judiciary Committee next year, told CNN Sunday that if the president was involved in criminal campaign-finance violations, “that might very well be an impeachable offense.”

Asked about the Journal’s report, Mr. Nadler said it would be a question of whether Mr. Trump’s involvement could be proved and “whether the situation is serious enough that it makes sense to do an impeachment to defend the system of government and the system of democracy.”