Arguelles, a Cuban defector, has been in Surprise, Ariz., since he reported for Spring Training and has not yet pitched for a team in the organization.
"But he's seen two different doctors and everybody thinks he's going to be fine," general manager Dayton Moore said Friday.
The Royals had Arguelles cut back during Spring Training because he'd thrown extensively for months as he auditioned for Major League clubs. Now the question is will he be ready to pitch in the Minor Leagues before the season is over?
"We expect him to, but we'll see how that plays out," he said.
Moore said another top left-handed prospect, Mike Montgomery, has had some tricep tightness in his throwing arm but that it's not believed to be serious.
Montgomery, who last pitched on May 27, has a 3-1 record and a 2.84 ERA in five starts for Northwest Arkansas.