Santana, who turns 31 on Dec. 12, is seeking a multi-year contract that FoxSports.com has reported to be five years and $100 million.
If Santana signs with another club, the qualifying offer nets the Royals an extra pick in the First-Year Player Draft's compensatory round between the first and second rounds next June.
Santana, obtained in a trade from the Angels last winter, completed the $13-million option year of a five-year deal in 2013. He was 9-10 for the Royals with a 3.24 ERA over 32 starts and 211 innings.
The Royals can still negotiate with Santana, but his reported price range and long-term aspirations seem to conflict with general manager Dayton Moore's inclination to avoid such contracts with older players.
Even so, the Royals reportedly are interested in right-hander Tim Hudson, 38, a free agent from Atlanta whose season was ended by a broken right ankle in July. Before that, he was 8-7 with 3.97 ERA in 21 games. Whether the Royals would risk going beyond one year for Hudson remains to be seen. The Orioles and Indians also supposedly have interest.
The other players turning down the qualifying offers were Carlos Beltran, Cardinals; Robinson Cano, Curtis Granderson and Hiroki Kuroda, Yankees; Shin-Soo Choo, Reds; Stephen Drew, Jacoby Ellsbury and Mike Napoli, Red Sox; Ubaldo Jimenez, Indians; Brian McCann, Braves; Kendrys Morales, Mariners, and Nelson Cruz, Rangers.
For most players, long-term security is apparently the overriding concern over big bucks for a single year.
Last year all nine players who were made qualifying offers of one year for $13.3 million turned them down. Eight of them subsequently signed multi-year contracts although five got annual salaries that averaged under $13.3 million.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.