The 29-year-old right-hander was acquired by Kansas City in a midseason trade with Cincinnati this year. He went a combined 11-13 with 3.44 ERA.
He struggled during the regular season after the trade, going 4-7 with a 4.76 ERA but was 2-1 in the postseason. Cueto became the first American League pitcher since 1991 to throw a complete World Series game, a two-hitter against the New York Mets in Game 2, when he retired 16 of the last 17 batters he faced.
In 2013, Cueto went 20-9 with the Reds, leading the National League in strikeouts (242), starts (34) and innings pitched.
The rejection of the offer first was reported by MLB.com.