Kuroda underwent a battery of tests that indicated he was recovering from the line drive he took on his head on Saturday in Arizona, but was sent home early and missed his previously scheduled bullpen session.
"That would all but eliminate that," Torre said of Kuroda taking his next turn in the rotation.
Trainer Stan Conte said that Kuroda continues to experience headaches from time to time and that his activities will be determined on a day-by-day basis.
Kuroda underwent an exam that tests brain function, and it showed he had a mild concussion.
"A lot of his reaction times were normal," Conte said. "It was a very good indicator for us that things weren't really bad."
Kuroda also rode a stationary bicycle and his symptoms didn't worsen when his heart rate increased, something else Conte took as a sign of progress. Kuroda will undergo more tests today.
"Absolutely," Padilla's agent, Paul Kinzer, said. "To be in a pennant race, he's definitely interested."
Padilla will become a free agent on Wednesday and can be signed for a prorated share of the league minimum, which is $400,000. The Rangers remain on the hook for the remainder of his $12-million salary.
A source in the Dodgers' front office said a Padilla signing was "unlikely at the moment."
Padilla was 8-6 with a 4.92 earned-run average and has developed a reputation as a bad teammate.
The Dodgers continue to comb the waiver wire for arms to add to their depleted pitching staff.
John Smoltz was recently released by the Boston Red Sox and is also available for a prorated share of the league minimum, but the Dodgers have serious concerns about his surgically repaired shoulder.
New number for Ohman
Left-hander Will Ohman, who gave Randy Wolf his No. 43 uniform, will be wearing No. 77 when he returns from the disabled list, prompting Mark Loretta to call him "Agent O-double-seven."
"I should be computing in style," said Ohman, who didn't receive anything from Wolf.
Ohman will begin a minor league rehabilitation assignment today by pitching an inning for Class-A Inland Empire. He is scheduled to pitch for Inland Empire again Thursday.
Back in order
A nearly monthlong slump prompted Torre to move Hudson down in the order, but the second baseman went into Monday's game having reached base safely in 15 consecutive starts.
Hudson was two for five with a home run as the Dodgers' No. 2 hitter on Sunday hitting behind Matt Kemp.
"I think the biggest thing with O-Dog is keeping him from thinking he has to do too much," Torre said.
Jason Schmidt has resumed throwing at the Dodgers' spring training complex in Arizona but remains a longshot to pitch again this season. . . . The Dodgers are holding an online auction at dodgers.com/thinkcure to raise money for cancer research. The auction ends Monday.