Manager Bud Black said there's a "high probability" Alonso will be reinstated from the DL in time to start Friday against the Giants at Petco Park.
Alonso, who landed on the DL on June 6 (retroactive to May 31) with a fracture in his hand, played in his fourth Minor League game with Triple-A Tucson on Thursday as part of his rehabilitation assignment.
Alonso, who had six hits in his first 11 at-bats with Tucson, was hitting .284 in 54 games with six home runs and 29 RBIs before landing on the DL.
"Physically, he's doing well," Black said. "The hand is fine, there's no pain. The swings are better. He's gotten some hits, not a lot of them hard contact. But he swung the bat better last night, he used his lower half and it's much more indicative of the swings we expect when he comes back."
Second baseman Jedd Gyorko -- on the disabled list since June 10 with a strained right groin -- had two hits in his first rehabilitation game Wednesday with Class A Lake Elsinore. He will play Thursday for the Storm and then Friday with Tucson in a game in Las Vegas.
Black was asked why he wouldn't consider simply allowing Alonso and Gyorko to sit these last games before the All-Star break then turn them loose in the second half.
"Every game is important; if guys are healthy and we think they're ready to contribute and help us win, we'll pull the trigger," Black said. "But we've got to first make sure everyone is ready. It's why we have put a lot of eyes and a lot of observations on our players."
The Padres will need to make some notable moves in order to get Alonso and Gyorko back on the roster. Black said the team was still going through its options as of Thursday afternoon.