WASHINGTON—Democrats will seek a firsthand look at President Trump’s tax returns if they take control of the House or Senate after next month’s election, according to the key lawmakers who would gain the authority to get the documents.

Rep. Richard Neal (D., Mass.), in line to lead the House Ways and Means Committee if Democrats win that chamber, said he would get the documents, which the president has declined to release voluntarily.

“Yes,” Mr. Neal said when asked if he would request the returns. “We will do that.”

Sen. Ron Wyden (D., Ore.) followed Mr. Neal on Wednesday, saying for the first time that he would request the tax returns if he became Finance Committee chairman in January.

Mr. Trump’s tax returns aren’t a big part of Democrats’ midterm campaigns, but they were a significant issue during the 2016 presidential election. House Democrats have repeatedly tried to get Congress to use its existing authority to obtain the returns, failing on more than a dozen votes since his inauguration.