Cordero was designated for assignment by the Nationals on Monday, Jorge Castillo of The Washington Post reports.
Cordero was ousted from the 40-man roster to clear room for Brandon Kintzler, who was acquired from the Twins on Monday. The 25-year-old struggled to a 6.54 ERA and 1.76 WHIP in 42.2 innings with Double-A Harrisburg this season, so there's a good chance he'll slip through waivers untouched and return to Double-A.