Morse, who is on the disabled list because of a torn left lat, is hoping to play his first Major League game of the season on June 8, when the Nationals play the Red Sox at Fenway Park. He would serve as the designated hitter in the American League park.
Meanwhile, infielder/outfielder Mark DeRosa, who is on the disabled list because of a left oblique strain, is expected to start throwing on flat ground on Wednesday. He hopes to start hitting by the end of the week.
"I'm starting to get to the point of being pain free. Now we just have to ramp it up and get a bat in my hand. I feel good," DeRosa said.