The 37-year-old is 6-10 with a 4.15 ERA and 123 strikeouts in 149.2 innings this season for the Phillies.
Burnett's current contract runs through the 2014 season, but he does have a mutual/player option for 2015 tied to his contract.
The Royals are 54-52, five games back of the American League Central-leading Detroit Tigers. The team is also 3.5 games out of the second American League wild card spot.
- Sarah Barshop