The Royals are still in the running for the best record in the American League, but despite only trailing Toronto by one game, the Royals essentially need to make up two games in the final four since the Blue Jays hold the edge in the regular season series 4-3. A tie will favor Toronto.
Assuming the Royals finish second overall and the Texas Rangers hold off the L.A. Angels and Houston Astros for the West Division, I think the safe bet is that the Royals will open the American League Division Series against the Rangers.
Here is the ALDS schedule:
Game 1-Thursday October 8th-Kauffman Stadium-TBD
Game 2-Friday October 9th-Kauffman Stadium-TBD
Game 3-Sunday October 11th-TBD
Game 4-Monday October 12th-TBD*
Game 5-Wednesday October 14th-Kauffman Stadium-TBD*