Per Heyman, Oakland presented Encarnacion with a $50 million deal before he settled on a three-year, $60 million offer from Cleveland.
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Trumbo, a native of Anaheim, Calif., would be a major boost to the A's lineup after setting a career high with 47 home runs with the Orioles in 2016.
The Orioles had a four-year offer on the table for Trumbo earlier this offseason, and though they have since rescinded that offer, they are still reportedly interested in bringing him back.
The Rockies have also been linked to Trumbo, who also set a career high with 108 RBIs and was selected to the American League All-Star team in 2016.
Oliver Macklin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.