Billingsley said he threw at 85 percent Friday and would conduct the acid test Saturday.
"Tomorrow will be the bigger one. I'll go game speed and see if it holds up," said Billingsley, who injured the left hamstring coming out of the batter's box a week ago. "Today was the first time I did agility and jogging and it felt good."
Billingsley said the tape that encases his thigh does not restrict movement in his windup or delivery.
Torre has not announced a probable starter for Tuesday, essentially the fifth starter's day to pitch. But the Dodgers, at this point, really don't have a fifth starter. Jeff Weaver could get the call, assuming he doesn't make the start in place of Billingsley, as he did Wednesday.
The Dodgers also could call up Eric Stults or Scott Elbert. Or they could acquire a pitcher, although general manager Ned Colletti said his conversations with other clubs indicate a game of cat-and-mouse until the urgency of the end of the month, the deadline for acquired players to be eligible for the postseason.
Vicente Padilla and John Smoltz also are expected to be available as free agents and the Dodgers have had internal discussions about both.
In other pitching news, the Dodgers got their first look in a while at disabled reliever Will Ohman, who threw a bullpen session and reported no trouble with a flexor tendinitis that has had him sidelined the better part of three months.
"I couldn't pinch a nasal spray bottle," he said of the pain he experienced with an injury suffered while recovering from a stiff shoulder. "Everything's as healthy as I could have hoped for. No pain or discomfort. I assume my next stop is game competition."
Ohman, signed a week before the season started, acknowledges that the injury is probably the result of rushing to be ready without the benefit of a full Spring Training. Torre said Ohman would soon begin a Minor League rehabilitation and probably wouldn't be activated until September, when the rosters expand.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.