Duke was released by the Reds on Saturday.
Duke was designated for assignment by the Reds on Monday.
Duke (calf) was reinstated from the 10-day injured list Friday.
Duke (calf) is expected to return from the 10-day injured list ahead of Friday's series opener against the Nationals, John Fay of The Cincinnati Enquirer reports.
Duke landed on the injured list Monday with a right calf sprain.
Duke gave up one run over two innings in Friday's loss to the Dodgers, with the run coming on a homer by lefty Cody Bellinger.
Duke retired just one batter Thursday night and allowed a two-run homer to Freddie Freeman.
Duke walked in a runner and allowed two more inherited runners to score on a single in Sunday's loss to the Cardinals.
Duke was awarded the win on Opening Day on Thursday against the Pirates after retiring the two batters he faced.
Duke gave up two runs in an inning Tuesday against the White Sox, raising his spring training ERA to 4.91. He's competing with Cody Reed, Wandy Peralta, Matt Wisler among others for one of the final two bullpen spots with the Reds, Mark Sheldon of MLB.com reports.