TAMPA, Fla. — Boston manager John Farrell said Red Sox left-hander David Price has increased strength in his sore pitching elbow but isn't ready for a "full-blown throwing program."

Price was re-evaluated before the Red Sox played the New York Yankees on Tuesday night.

"Strength gains have been had, but we're going to continue to stay in the strength and conditioning phase of this," Farrell said. "He'll continue to get his arm moving in the cage, in the workout room and the training room. We're getting closer."

Farrell didn't rule out Price increasing his throwing later this week.

Starting the second season of a $217 million, seven-year contract, Price has not appeared in an exhibition game and is expected to begin the season on the disabled list.

Price, the 2012 AL Cy Young Award winner with Tampa Bay, was 17-9 with a 3.99 ERA last year. He felt discomfort in his left elbow after a two-inning simulated game on Feb. 28.