Rosales, who is nursing an intercostal strain, may be ready for one as soon as Thursday, when the team departs for Tampa, as long as he is no longer experiencing pain when throwing across his body.
Nakajima (hamstring) may not be too far behind him, but he needs to show he can run the bases first before he returns to any game action.
"If he runs the bases this weekend, then maybe we're closer with him as well," manager Bob Melvin said Monday. "You have good days and bad days, and there are days he hasn't felt great. When we were on the road trip, I think there were a couple days he wasn't making progress, but here recently he's said he feels very good, so I think we're on the verge of getting him on the bases. We'll have a better indication of where he is once he does that."
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.