Price figures to file the highest figure unless his case settles before Friday's exchange. The 2012 AL Cy Young Award winner made $14 million last year when he started the season with Tampa Bay and finished with Detroit.
Baltimore first baseman Chris Davis is likely to file for the highest amount among position players. The 2013 major league home run champion had a $10.35 million salary and earned a $150,000 performance bonus last year, when he served all but one game of a 25-game suspension for a positive test for Adderall, a banned amphetamine.
Five players on the Toronto Blue Jays filed for arbitration: pitchers Brett Cecil and Marco Estrada, infielders Josh Donaldson and Danny Valencia as well as Canadian outfielder Michael Saunders.
Other who filed included Kenley Jansen, Austin Jackson, Mark Trumbo and Matt Wieters.
Catcher A.J. Ellis reached an agreement Tuesday with the Los Angeles Dodgers at $4.25 million, a $700,000 raise.
Hearings will be scheduled for the first three weeks in February before three-person panels in St. Petersburg, Florida.
Just three of the 146 players who filed last year went to hearings, with Cleveland defeating pitchers Vinnie Pestano and Josh Tomlin in the Indians' first cases since 1991 that went to hearings. Pitcher Andrew Cashner beat San Diego.
The three decisions matched 2005, 2009 and 2011 for the second fewest in a year. The number of hearings peaked at 35 in 1986, and there were none in 2013.
Teams have a 293-215 advantage since the process started in 1974 and have had a winning record in 15 of the past 17 years with decisions.