Headley, who fractured the tip of his left thumb on March 17 during a Spring Training game, played in his fourth Minor League game in five days on Tuesday, playing for the Class A Lake Elsinore Storm.
San Diego manager Bud Black was asked if Headley could be at Dodger Stadium on Wednesday.
"Possibly," Black said. "We're going to see how it goes tonight."
Either way, Headley isn't far off. If he doesn't return Wednesday, he'll most certainly be back in the lineup on Friday when the Padres open a three-game series in San Francisco.
In his first three Minor League rehab games, Headley hit .222 (2-for-9). On Tuesday, he was scheduled to face Dodgers pitcher Ted Lilly, who is on a Minor League rehab assignment with the Rancho Cucamonga Quakes.
Black said he had a conversation with Headley on Tuesday morning and Headley informed him that he was tested in the field.
"He's close," Black said.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.