Cook, 28, has pitched in the Majors for parts of five seasons with solid overall numbers. Acquired by the A’s from the D’Backs in the December 2011 Trevor Cahill trade, Cook made the All-Star team in 2012 and saved 14 games. However, he missed time with a shoulder injury and forearm strain last year, and was optioned to Triple-A out of spring training. That’s where he’s spent most of this season, compiling a 4.05 ERA in 33 1/3 innings. The Red Sox will potentially control Cook through 2018 as an arbitration eligible player.