The Royals began the playoffs by defeating the Oakland Athletics and pitcher Jon Lester in the AL Wild Card game, then swept the Angels in the ALDS.
Lester will join Shields on the market this offseason.
In each of the last eight seasons, Shields has pitched at least 200 innings, the only pitcher in the AL to do so. This season he posted a 3.21 ERA with 180 strikeouts and 44 walks in 227 innings.
His efforts helped the Royals end the regular season with an 89-73 record and a second place finish in the AL Central.
In game three of the ALDS against the Angels, Shields held Los Angeles to two runs in six innings.
The Royals will reportedly offer him a new deal worth $80 million over five years after the conclusion of this season.
However, according to McCullough, rival executives expect that he will receive multiple offers ranging between $80 and $110 million for five years during his free agency.