Crawford, who has a sprained UCL in his left elbow, has progressed to taking batting practice. He's not been cleared to throw, but that's next in his recovery process.
"Probably the end of this week is what the plan was," said manager Bobby Valentine.
Ellsbury, though, is playing catch and has progressed to 40 throws. Out since April 13 with a separated right shoulder, Ellsbury has made strides in recent weeks.
"He's hitting off the tee, he's running the bases. It will be a normal progression barring any setbacks," Valentine said, "but he's feeling great. Eventually we'll have him do real activities, [including] batting practice."
Ellsbury missed his 50th game on Thursday in the series finale vs. the Orioles. Crawford has not played this season.
Boston has used nine different outfielders since Ellsbury's injury, including first baseman Adrian Gonzalez in right field.