U.S. Rep. Marcia Fudge of Ohio, leader of the group, made the request in a letter to Obama Monday, the McClatchy Newspapers reported Thursday.
McClatchy said it obtained a copy of the letter.
"Congressman Clyburn's legacy of public service to the American people and to the citizens of his congressional district is one of honor and distinction," Fudge said in the letter.
An aide to the congresswoman told McClatchy Wednesday she hadn't received a response. White House aides did not respond to requests for comment.
Clyburn, 72, the House assistant Democratic leader, "is proud and honored that some of his colleagues think enough of him to recommend him for transportation secretary, but the only job change Mr. Clyburn is working on is once again becoming [House] majority whip when the American people reject the Republicans' failed leadership and extreme partisan gamesmanship and Democrats win back the House," said Patrick Devlin, a Clyburn spokesman.
Transportation Secretary Ray LaHood, a Republican and former congressman from Illinois, announced plans to leave the post last week.