Mica was reelected to an 11th term in Congress in last week's election. He has been chairman of the Transportation and Infrastructure Committee since 2010, but he is facing term limits for committee chairmen set by House Republicans when they took control of the lower chamber.
The rules call for lawmakers to step down after six years as ranking member or chairman of a particular committee, unless they are given a waiver by leadership.
The lawmaker who has been widely expected to replace Mica atop the transportation panel, Rep. Bill Shuster (R-Pa.), has formally announced his candidacy and sounded notes that he is expecting to be chairman.
Mica said Tuesday that the transportation committee chairman issue "should be over by Thursday."
He said of BoehnerJohn BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection MORE: "He'll have to decide what he's going to do, and then I'll have to decide what I'm going to do."