TORONTO — Greg Bird and Starlin Castro took significant steps in their respective rehabs on Tuesday.

Each did some light running and took batting practice several hours before the game against the Blue Jays, with Bird in particular putting on a show during BP with a handful of long home runs.

After BP, the pair did field work with infield coach Joe Espada.

“Feeling really good where I’m at,” said Bird, adding later that “ideally” he’ll be declared ready to start a minor league rehab assignment by the end of the Yankees next homestand, Aug. 15.

Bird’s season never really got going after he fouled a ball off his right ankle March 30 during the Yankees’ last game of the Grapefruit League season, causing a bone bruise that troubled him throughout most of April and landed the first baseman on the disabled list May 2. But the 24-year-old has progressed steadily since surgery on the ankle in mid-July and has maintained since the operation that he planned to play again this season.

Castro has been on the disabled list since July 22 with a right hamstring strain, the same injury that caused him to miss 13 games from June 27 to July 14.

“He’s progressing,” Joe Girardi said of Castro, though he declined to give a timetable for when the second baseman might be ready for a rehab assignment. “He looked good.”

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Montgomery rationale

Girardi said among the reasons LHP Jordan Montgomery was optioned to the minors Sunday was an innings limit for the rookie that’s in the neighborhood of 180. Girardi said that Montgomery will continue to start at Triple-A but will have some outings “shortened.” Montgomery has thrown 115 2/3 big-league innings this season.

Hicks getting there

Girardi said OF Aaron Hicks, whose rehab assignment continued with Double-A Trenton Tuesday, is “pretty close” to ready and that “it’s possible” he will be activated in time for the Boston series this weekend.