Wilson is scheduled to make another appearance on Tuesday and is eligible to come off the disabled list on Wednesday, but the club wants to see how his surgically repaired elbow responds to pitching on consecutive days.
If all goes well, he could join the Dodgers during their seven-game road trip, which begins on Friday.
"I want him to be comfortable when he comes up," manager Don Mattingly said on Sunday. "We want him to be ready and want him to feel like he's ready."
The Dodgers signed Wilson, 31, as a free agent on July 30. The former Giants closer has not pitched in the Major Leagues since undergoing Tommy John surgery in April 2012.
Ken Gurnick is a reporter for MLB.com. Austin Laymance is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.