OAKLAND -- The clock is ticking on Matt Kemp being healthy enough to play in the All-Star Game.

Kemp is the National League leading vote-getter and a slam dunk to win a starting spot through fan balloting. But except for one game, he's also been on the disabled list twice since May 14 with a strained hamstring. His recovery is going nicely, as it did the first time, only for him to blow a tire his first game back.

The July 10 All-Star Game in Kansas City (350 miles from his Oklahoma hometown) is three weeks away. When Kemp was reinjured May 29, the prognosis was a month on the shelf. Trainer Sue Falsone still holds to the vague timetable of a return "around the All-Star break."

She also said on Tuesday, however, that the club wants Kemp to have a longer Minor League rehab assignment than the two games he played before his May 29 activation.

Manager Don Mattingly repeated Tuesday a previously expressed desire that Kemp would be healthy enough to play in Major League games for the Dodgers before making an All-Star appearance. The last thing anybody in the organization wants is for Kemp to rush back to play in the All-Star Game, break down for a third time and jeopardize the team's chances.

Kemp is captain of the NL team in the Home Run Derby and is expected to participate in that competition regardless.

"The All-Star Game is a discussion we need to have," Mattingly said. "It's a tough call if he's not able to play in a game for us. I know he'd like to play. We'll talk as an organization and talk to Matt."

Ellis upbeat about progress from leg injury

OAKLAND -- Dodgers infielder Mark Ellis won't say he's ahead of schedule in his recovery from an unusual and painful lower left leg injury, because he never had a schedule.

But he did say Tuesday that the progress has been steady and he's eager to return. He's begun to sprint and take grounders, will run the bases this week and now is focused on regaining his hitting stroke.

"The big thing was getting over the mental hurdle that it wasn't going to break down," Ellis said. "I did that pretty quick. There's no discomfort. The knee it not bothering me at all and that's a really good sign. I'm further along than I thought at this point. Every day I'm getting a little better, but I still don't know when I'll be playing."

Ellis had an emergency fasciotomy May 20 to relieve swelling pressure in the leg and also suffered a sprained medial collateral ligament in his left knee and a bone bruise below the knee from a take-out slide by St. Louis' Tyler Greene.

He has an eight-inch scar still pink and healing from the surgery, necessitated when it was determined that a muscle had been cut, causing bleeding that was trapped by the muscle sheath. Doctors that performed emergency surgery said he could have lost the leg without it.

Ellis was pleased to make the trip to Oakland, where he played for 10 years.

"I've got so many friends here -- not only players but security guards and clubhouse staff. It's good to be back," he said. "It feels a little weird to be back on the other side."

Lilly could resume throwing by end of week

OAKLAND -- With management on the prowl for a starting pitcher, one of the reasons that's necessary, injured starter Ted Lilly, finally reported some semi-good news.

"They're not sure, but they're talking about Lilly maybe throwing at the end of the week," Dodgers manager Don Mattingly said Tuesday. "That's a little positive. He's feeling better."

Lilly hasn't felt well enough to throw since being placed on the disabled list May 24 with left shoulder inflammation.

In response, the Dodgers have been looking to trade for a starter, with Cubs right-hander Ryan Dempster most frequently mentioned until he went on the DL on Monday with a strained lat muscle.

Mattingly said he was hoping to get Matt Kemp (hamstring), Mark Ellis (leg surgery) and Javy Guerra (knee surgery) back "quickly after the All-Star break."

Round of golf with Capuano up for auction

OAKLAND -- A round of golf with Dodgers starting pitcher Chris Capuano at legendary Torrey Pines in La Jolla is one of the unique player-related experiences up for bid on a fundraising auction for Players Trust.

Bidding for the current lot of available auction packages on CharityBuzz.com ends Thursday between 9:05 a.m. and 10 a.m. PT. Proceeds from the auction benefit initiatives of the Players Trust, the 501(c)(3) charitable organization created and administered by the players themselves.

For a complete list of items currently up for bid during the Players Trust auction, visit: www.charitybuzz.com/search?keywords=players+trust.