Upton jammed his left thumb while sliding into second base in the first series of the season against the Giants, and it has bothered him since.
"Every morning when I get up it's a little better, which is a positive sign," Upton said. "I don't want to re-irritate it and have it come back. The good thing is that it's getting better every day, so we'll see how it is tomorrow."
With fellow outfielder Chris Young out with a shoulder injury, the D-backs could certainly use Upton's bat in the lineup.
"To be honest with you, I feel like I'm close," Upton said.
Initially, Upton tried to play through the pain, but it clearly was taking a toll on his performance.
In his first 40 plate appearances this year, Upton hit .212 with two doubles and no homers or RBIs.
"It's not fun, and I think it got to the point where I wasn't helping anybody," Upton said. "I wasn't helping the team, so I figured if I could get it right, that's better for me and the team."