Alonso hit in the cage and on the field before Tuesday's game at Dodger Stadium and said the strength in his right hand is better than it's been since he was hit by a pitch on Friday.
"It's getting better, much better," Alonso said before the game. "It's healing a lot faster than I thought it would. I think I'll be in there soon."
Alonso could be back in the lineup for the series finale Wednesday against the Dodgers. Jesus Guzman got the start at first base on Tuesday night.
"We're headed in that direction," said Padres manager Bud Black.
Alonso was hit on the hand by a pitch in the Padres' 17-inning victory over the Jays on Friday and has not had an at-bat since. Black did say Alonso was available to pinch-hit Tuesday.
The biggest issue that Alonso has faced since he was hit is having strength in the right hand to swing a bat. He tried unsuccessfully to do so Monday, but his hand felt strong enough to swing the bat prior to Tuesday's game.
Alonso liked how he felt and liked the results.
"It was the same old swing," he said. "I feel like I'm close to coming back."
Alonso is second on the team with a .284 average and is second in hits (54) and leads the Padres with 29 RBI's.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.