Manchin is scheduled to present his appointee at a Friday afternoon press conference at the Capitol.
Goodwin served as Manchin's general counsel from 2005 until early 2009.
Goodwin would hold the seat until November, when the governor wants general election voters to decide who will serve the final two years of Byrd's term.
Byrd was the Senate's longest-serving member when he died last month at 92.
