The Rays' center fielder will start the season on the disabled list due to a lower back problem.
Upton sounded optimistic on Monday that he won't miss too much regular-season action.
"I threw yesterday and ran yesterday," Upton said. "And I was able to do that before, it just bothered me the next day. And now it's fine, so that's a good sign."
Initially, Upton had hoped to be ready for Opening Day, but the Rays decided to back off on that goal in order to make sure the problem doesn't linger. Upton believes that was the right call.
"I wanted to be back for Opening Day," Upton said. "I think everybody as a whole, we were just trying to get me ready for Opening Day, and that may not have been the thing to do with the situation. I'm glad we just let it rest, and it's getting better. That's all we can ask for now."
Upton believes he will be back with the team at some point during its three-stop road trip that begins in Detroit on April 10.
Rays manager Joe Maddon pointed out that Upton needs at-bats before he can be ready to play again.