Cardinals ace Adam Wainwright chimed in on Sunday via Twitter.
Cubs manager Joe Maddon was going to let someone else make the decision regarding expanding the current format.
"That's above my pay grade right there," Maddon said.
Some pitching coaches might be cringing at the thought of having their hurlers risk injury if they're swinging for the fences. Not Maddon.
"Everybody's afraid of injuries," Maddon said. "Everybody's afraid everybody's going to get hurt every day. I don't subscribe to that theory, so I don't worry about it."
However, if there was a pitchers' version, Maddon would like to see it scaled down and not a "full gorilla Home Run Derby."
Some of the possible candidates besides Bumgarner and Arrieta could include the Mets' Noah Syndergaard and Jacob deGrom and the D-backs' Zack Greinke. Who would be Maddon's pre-Derby pick?
"[Arrieta] is strong, man," Maddon said. "Bumgarner has a great swing. He's got a real swing. Jake's good, but Bumgarner is really loose and free and easy with his approach."
Cubs first baseman Anthony Rizzo, who took part in last year's Home Run Derby along with teammate Kris Bryant, said on Sunday that he hadn't talked to Arrieta about whether to swing or not.
"I'd probably advise him not to do it," Rizzo said. "It's just different -- Why mix it up?"
"It was a great experience," Rizzo said. "Pitchers don't swing as much. They swing five times every five days."
Arrieta already is anticipating a crazy adrenaline rush.
"People think we can't hit," Arrieta said. "We'll show you we can hit home runs."
Carrie Muskat has covered the Cubs since 1987, and for MLB.com since 2001. She writes a blog, Muskat Ramblings. You can follow her on Twitter @CarrieMuskat and listen to her podcast. This story was not subject to the approval of Major League Baseball or its clubs.