The Browns could find many willing parties to pick up a deal, as the Buffalo Bills, Tennessee Titans, New York Jets, and San Francisco 49ers are among several teams looking to trade down in the current first-round order.
Cleveland also holds pick No. 33 and pick No. 52.
Browns general manager Sashi Brown recently told the NFL Network that the franchise isn't "desperate for a quarterback."
Brown also said that the team has known who the No. 1 pick for two weeks, according to CBS Cleveland.