The report also notes that some league executives believe any offer of that magnitude would be surprising, considering Shields is 33 years old and coming off eight consecutive seasons of 200-plus innings.
The latest news leaves the market for Shields unclear, as several teams would likely bow out of the running for Shields at the expected price.
MLB.com's Joe Frisaro tweeted Sunday night that the Marlins would be among the clubs backing off their pursuit of Shields at that price, and the Fox Sports report also lists Arizona, Boston, San Francisco, San Diego and Kansas City as now unlikely landing spots for the veteran right-hander.
Shields, who received a qualifying offer from the Royals in November, went 14-8 with a 3.21 ERA last year for Kansas City, helping the Royals reach the World Series.
Chad Thornburg is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.