The committee's top job will be open when current Chairman Dave Camp. R-Mich., steps down because of term limits, Roll Call said.
Rep. Kevin Brady of Texas is the second-ranking Republican on the Ways and Means Committee, which handles tax-writing and budget duties in Congress. He also heads the Joint Economic Committee.
Ryan, chairman of the House Budget Committee, is third-ranking Republican on the committee and was the Republican vice presidential candidate in 2012.
"He's a terrific leader, a good friend," Brady said of Ryan in an interview with columnist Al Hunt to be broadcast on Bloomberg TV, Roll Call reported. "But the point is, I'm qualified and prepared to lead this committee."
Roll Call obtained a transcript of the interview.