Greinke wouldn't identify the other club, but the question was about his former team, the Los Angeles Dodgers, and he answered with a smile, so it seems it was not hard to decipher.
Instead of re-signing with the Dodgers, Greinke listened to the Diamondbacks' pitch. He liked it, and a deal was put together the following day.
The Diamondbacks, long considered a small-market team despite playing in the nation's sixth-largest city, acquired the most accomplished free-agent pitcher on the market.
"I'm glad we were a minute too soon than a minute too late," Diamondbacks general manager Dave Stewart said Friday at Greinke's introductory news conference.
Greinke, this year's NL Cy Young Award runner-up, also was sought by the NL West rival San Francisco Giants.
Greinke pitched in Los Angeles the past three seasons and was 19-3 with a 1.66 ERA this year, the best ERA among big league qualifying pitchers since 1985. The 32-year-old right-hander narrowly missed a second Cy Young, finishing behind the Chicago Cubs' Jake Arietta.
Greinke, who won the 2009 AL Cy Young while with Kansas City, said he was all set to sign with another team when he received a call from his agent about the Diamondbacks.
"That got me excited," Greinke said.
The sides agreed to a $206.5 million, six-year contract that has the highest average annual salary in baseball history at $34.4 million. The deal includes $62.5 million in deferred money that lowers its present-day value to $193,849,298, according to the calculation by Major League Baseball.
It was a bold move for the Diamondbacks, who have primarily stuck to midlevel contracts since signing Randy Johnson in 1998. Arizona wasn't done, either, trading 2015 No. 1 overall draft pick Dansby Swanson and outfielder Ender Inciarte to Atlanta in a deal for All-Star right-hander Shelby Miller.
The spending shift followed a $1.5 billion TV deal signed with Fox Sports Arizona last February that will span more than 20 years.
"It puts us in a place where we could be more financially competitive," Diamondbacks Managing General Partner Ken Kendrick said. "We felt like there was a window to compete to make significant improvement to our rotation ... and the stars aligned."
The thought of playing for Arizona occurred to Greinke during a series in the desert just before this year's All-Star break. He noticed how hard the scrappy Diamondbacks played, the way they played defense and how they knocked the ball around Chase Field.
"I was just thinking, like, 'Man, they have something going on there,'" Greinke said. "Just need a couple things and could be as good as anybody."
First baseman Paul Goldschmidt was second in NL MVP voting for the second time in three years, and outfielder A.J. Pollock was an All-Star in 2015. Arizona scored the second-most runs in the NL last season while playing in one of baseball's most hitter-friendly ballparks.
The Diamondbacks also have solid core of young infielders and outfielders, combining to form one of baseball's best defensive teams.
Arizona has some talented pitchers in its rotation, including left-hander Patrick Corbin, who returned from Tommy John surgery last season. The Diamondbacks just didn't have a top-of-the-line starter.
That changed this week with the additions of Greinke and Miller.
"We liked our position players going forward and felt like with our young arms, a rotation leader was the No. 1 thing that could help us," Diamondbacks chief baseball officer Tony La Russa said. "We were fortunate to get one like Zack."