David Price said Saturday he could start throwing in the coming days but is unsure when he will return from the first disabled list stint of his major league career.

On May 16, the Tampa Bay Rays left-hander and reigning American League Cy Young Award winner was placed on the 15-day disabled list following a left triceps strain sustained in a 2 1/3-inning outing in a loss to the Boston Red Sox the day before. Price said he has participated in arm and shoulder exercises, in addition to sock throws in which he holds a ball and throws it in a sock, as if mimicking his throwing motion.

"I honestly have no idea," Price said of a timetable for his return, before the Rays played the New York Yankees in the second game of a three-game series at Tropicana Field. "It probably all depends on how I feel when I play catch -- how all that happens and how I bounce back after that. It's not trial and error, but we just have to base it on day-to-day."

Price, who has a 1-4 record with a 5.24 ERA in nine appearances, did not travel on the Rays' most recent six-game road trip to Baltimore and Toronto. He said he has been bored in his down time and that "it felt like it was the offseason on a day where you come to the Trop and you do your arm exercises … and you go home."

Price said the hardest moment of his DL stint so far was watching right-hander Jake Odorizzi pitch Monday in his spot in the rotation. Odorizzi, called up from Triple-A Durham to start in Price's place until a return, gave up three runs and five hits in five innings in the Blue Jays' 7-5 victory at Rogers Centre.

Rays manager Joe Maddon said Saturday there were no further Price updates, but he added that there could be more information before the end of the Rays' current five-game homestand, which concludes Tuesday. Shortly after Price was injured, Maddon said he anticipated a "normal" DL stint for the pitcher, meaning two to three missed starts. Price can come off the DL as early as May 31.