If his improvement continues at the current pace, Hundley said he anticipates starting a Triple-A rehabilitation assignment Wednesday in Albuquerque.
"We're just going to see how I play ... get that rhythm and timing back," Hundley said. "I'm exciting about going to compete again."
Hundley went through a variety of baseball activities Monday under the watchful eye of Padres manager Bud Black.
"He's been increasing the work each and every day over the past week," Black said. "Today he threw the bases and ran. It's just a matter of getting him in game condition. He's very close."
Black estimated that Hundley will need more than five games on his rehabilitation stint.
"He's been out a while ... the conditioning aspect, we need to get him back and test the wrist, how he catches and how he hits to make sure there's no setbacks there," Black said.
Hundley, who went on the disabled list June 19 with a small fracture in his left wrist, said he consistently spends several hours per day undergoing treatments, such as ultrasound, muscle stem therapy and icing down the wrist.
At the time he went on the disabled list, Hundley was hitting .236 with 11 RBIs and 11 runs scored in 41 games.
"Physically I feel good, I feel strong," Hundley said. "It's definitely a grind mentally because I've been out for almost two months now. I've got to condition my mind to get back in there and be able to focus at that high of a level for so long.
"Once I can keep that focus for nine innings, I think I'll be ready to roll."
Amy Brittain is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.