Guillen and Baltimore's Jay Gibbons were suspended last Thursday by commissioner Bud Selig following media reports that they received human growth hormone after January 2005, when it was banned by baseball. Gibbons chose not to contest his penalty.
Arbitrator Shyam Das will decide whether Selig's suspension of Guillen was proper. The penalty is to be served at the start of next season.
"It's been agreed that the matter needs to be resolved prior to opening day," said Michael Weiner, the union's general counsel.
Guillen has not been charged by the government with a crime, and he is not known to have failed a drug test.
His could be the first of several grievances that will go before Das and could become a precedent for players disciplined for performance-enhancing drugs absent a positive test or a conviction for possession.
The San Francisco Chronicle reported last month that Guillen bought nearly $20,000 worth of steroids and human growth hormone from 2003-05. Major League Baseball began testing for steroids in 2003, and penalties for first offenses in cases involving performance-enhancing drugs began in 2005.
On the day he was suspended, Guillen finalized a three-year, $36 million contract with the Royals. The 31-year-old batted .290 with 23 homers, 99 RBIs and 28 doubles for the Seattle Mariners this season.