Price's $14 million salary in 2014 will be the highest single-season amount in franchise history. He earned $10,112,500 in 2013.
Price, who has one more season of arbitration eligibility in 2015, is scheduled to become a free agent after next season. He has been the subject of trade speculation this offseason.
In six years, Price has been a three-time All-Star, won the AL Cy Young Award in 2012 and finished second in the voting in 2010. Price is the Rays' career leader in ERA and winning percentage, and he is second in victories.
He was 10-8 with a 3.33 ERA in 27 starts last season. His 2013 season was interrupted by his first stint on the disabled list, caused by a strained triceps.
ESPN The Magazine's Buster Olney and The Associated Press contributed to this report.