The left-hander is considered day to day.
Asked if Downs could pitch Tuesday night, Scioscia said, "We'll evaluate to see his availability."
Scioscia did confirm, however, that Downs still hasn't thrown in the bullpen and that he's a question mark. As for whether Downs might wind up on the disabled list, Scioscia responded, "Right now, it doesn't look like a DL. Hopefully, he's made enough progress in the last two days that he's close."
Scioscia believes that he has enough arms for the two-game series against the White Sox.
"Hisanori [Takahashi] has pitched late in the game and he'd be available to do that," he said.
"Depending on how we match up, we have Fernando [Rodney] and [Bobby] Cassevah and, obviously, Jordan [Walden] in the back end, so we have arms that can get us in a position we want."