The media outlets, without specifying their sources, said Price and the team have avoided arbitration with a deal worth just over $10 million.
The 27-year-old three-time all-star was paid $4.35 million last season while he racked up a 20-5 record with an American League-best 2.56 ERA.
The left-hander has posted a 61-31 career record with a 3.16 ERA in 125 career appearances (including 120 starts) with the Rays.
Price also sports a 1-3 mark and 3.96 ERA in eight post-season appearances for the club.
UPI horse racing roundup