Darvish is scheduled to make three more starts before the break, including one that would come two days before the July 15 All-Star Game in Minnesota.
The Japanese pitcher shook his head "no" several times Thursday when asked whether he'd be willing to pitch an inning in the All-Star Game if he stays on that schedule. He then said through his translator that he'd go sightseeing while in Minnesota if on the AL squad.
All-Star pitchers who start the Sunday before the showcase game can be replaced on the roster by a fresh arm.
Darvish is 7-4 with a 2.62 ERA in 14 starts this season. He has 118 strikeouts in 96 1/3 innings.
The right-hander didn't pitch in the 2012 All-Star Game and was replaced on the AL roster last year because of injury.