The Bavarians secured their European crown with a 2-1 win over Madrid's semifinal conqueror Borussia Dortmund.
And Khedira, who is chasing an historic 10th Champions League trophy with los Blancos, has fired a warning to die Roten, insisting Carlo Ancelotti's men will be targeting them this year.
"Bayern Munich have to know that their international rivals intend on bringing back the balance," he told Welt am Sonntag. "They are the hunted now."
Germany international Khedira also believes the Liga outfit can look forward to progression under the tutelage of Carlo Ancelotti, who replaced Jose Mourinho as coach in June.
"It starts a new chapter for Madrid and at the same time in my career," he told AS. "A new coach is always associated with a new beginning. There are new ideas, a different playing philosophy.
"I feel a great excitement, I am still very proud to play for Real Madrid.
"Whomever plays at this club, playing for titles, I'm sure that with the work of Carlo Ancelotti we will take another step forward."
Although Khedira has never played under Ancelotti, he said Madrid playmaker Kaka has given the former AC Milan and Chelsea boss a glowing reference.
"I have heard a lot about Ancelotti," the 26-year-old continued. "Moreover, my teammate Kaka has worked many years with him in Milan, everything he said was positive.
"His teams have always played well. Such as with Paris [Saint-Germain] last year."