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7/1/2013 6:13 P.M. ET

Cabrera beginning rehab assignment Tuesday

MIAMI -- Shortstop Everth Cabrera begins a rehab assignment with Class A Fort Wayne on Tuesday. He will play games on Tuesday and Wednesday before he is re-evaluated.

The Padres could activate Cabrera as early as Thursday.

"There's a chance that he might get on a plane and meet us Thursday in Boston," San Diego manager Bud Black said. "Whether we activate him or not on that day is still up in the air."

If Cabrera is activated Thursday, Black said that he likely won't start the game that day against the Red Sox, because with the traveling, he might not make first pitch, which is at 10:35 a.m. PT.

"We could activate him if we wanted," Black said. "We'll see. That's granted if he comes out of Tuesday and Wednesday fine."

Grandal playing well through Miami homecoming

MIAMI -- Monday may be San Diego's fourth day of a 10-game road trip, but Yasmani Grandal feels right at home. The Miami product has been cheered on by his mother watching from the crowd during the Padres' four-game series against the Marlins.

"It's always good to play in front of family," Grandal said. "It feels great to be here and being able to play in front of them. It's been a pretty good weekend."

Grandal also managed to reconnect with Jim Morris, his former coach at the University of Miami. Grandal batted .401 with 15 home runs and 60 RBIs and finished second for the Golden Spikes Award in his final season under Morris in 2010.

"I haven't seen him in a while," Grandal said. "We got to talk a little bit and talk about last season and how they did and the expectations next year. I obviously follow them a lot."

Familiarity has led to continued improvement for Grandal, who is batting .380 (8-for-21) since June 20, raising his batting average from .179 to .234 entering Monday's game.

Grandal was 2-for-5 with three walks and three runs scored in two starts against Miami on Friday and Sunday. He started at catcher and batted sixth on Monday.

The 24-year-old credits his improvement to increased at-bats. Two inflamed tendons in the middle finger in his left hand prevented him from picking up a bat and swinging during the winter.

"[I'm] getting a feel," Grandal said. "[I'm] getting my body under control."

The switch-hitter aims to continue improving his average with a special focus on left-handed hitting. This season, he is batting .231 left-handed compared to his .279 career average when swinging lefty.

"I've been swinging it from the right side better than the left side, and that's really unusual for me," Grandal said. "I'm trying to get my lefty swing back on track."

Gyorko tests leg with running; no timetable for return

MIAMI -- Jedd Gyorko did some running during batting practice on Monday, but Padres manager Bud Black said there is still no timetable for the rookie's return.

"We're hoping, by the end of the week at least, he's back to moving around, running and getting closer to going back out to play a few more games," Black said.

"That's our anticipation. Nothing's imminent in the couple of days for him as far as any increased baseball activities."

Gyorko has been on the disabled list since June 10 with a strained right groin. He experienced tightness in his leg while running the bases during a rehab game with Double-A San Antonio on June 26.

The second baseman was looking forward to testing his leg before Monday's workout.

"It's getting better," Gyorko said. "Each day it's getting a little bit better."

Worth noting

• Injured first baseman Yonder Alonso had a CT scan on his fractured right hand on Monday. Padres manager Bud Black had not yet heard the results during batting practice before Monday's series finale against the Marlins.

When asked what he hoped the results show, Black said: "Just continued healing."

Black and the club are hopeful the the results will show enough progress to return to the batting cages soon.

Alonso has been on the 15-day disabled list since June 6. He suffered the injury when he was hit by a pitch in the seventh inning of the Padres' 17-inning, 4-3 victory over the Blue Jays on May 31.

Joe Morgan is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.