There had been widespread speculation that Greinke would opt out of the contract despite having three years and $71 million remaining on the six-year deal he signed with the Dodgers before the 2013 season.
Citing multiple sources in its report, CBSSports.com reported that Greinke should receive multiple contract offers of at least $125 million over five years, according to one general manager.
Greinke, who turns 32 on Wednesday, is coming off the best season of his 12-year career and figures to be a contender for the National League Cy Young Award. The three-time All-Star went 19-3 with a major league-leading 1.66 ERA this season.
Greinke emphasized that he was "not even thinking" about his future with the Dodgers after Thursday's season-ending loss to the New York Mets in Game 5 of the NLDS.
"It would be nice to be back [with the Dodgers]," Greinke said after pitching 6 ⅔ innings in Los Angeles' 3-2 loss. "I'm not even thinking about it. It's more about today, I guess. Maybe after I get home."
Information from The Associated Press was used in this report.