Wilson, who is 3-2 with a 2.70 ERA after a 4-3 victory over the Twins on Monday, is scheduled to pitch on Saturday against the Blue Jays.
His next start, if the weather doesn't alter the Angels' schedule, would be against the Rangers on May 11.
Wilson won 31 games as a member of the Rangers the past two years before he signed a five-year, $77.5 million contract with the Angels in the offseason.
Wilson is slated to be followed by Jerome Williams and Jered Weaver in the rotation. But the Angels could use the Thursday off-day and skip Williams, who is their fifth starter. Instead, they could follow Wilson with Weaver and Dan Haren.
Right now, the Rangers' rotation for the Angels series is set up to be Darvish against Wilson in Game 1, followed by Neftali Feliz and Matt Harrison.
"I haven't looked that far ahead," Rangers manager Ron Washington said before Tueday's game. "That should be a nice matchup. That means we should have a full house. I like it. Hopefully, we have some more distance between us and them by the time they arrive."
The Rangers had Feliz pitching on Tuesday and will have Harrison pitching Wednesday in the final two games against the Blue Jays.
This weekend, the Rangers have Colby Lewis, Derek Holland and Darvish lined up against the Indians. That leaves Feliz, Harrison, Lewis and Holland for the four-game series against the Orioles next week in Baltimore.