Yankees DH Nick Johnson started taking light swings with a bat off a hitting “T.’’

Six weeks ago this past Tuesday, Johnson underwent right wrist surgery. Though there is a lot of work to be done before the Yankees can count on him returning, Brian Cashman is hopeful the left-handed hitter can be back before August.

“All the reports have been good,’’ Cashman said. “We are hopeful at some time toward the end of a July we will have a player.’’

Johnson, who hasn’t played since May 7, could start a minor league rehab assignment after the All-Star break.

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According to Cashman, there is a chance outfielder Marcus Thames rejoins the club on the West Coast next week.

“We have to get the rust out and bring him up sooner than later,’’ Cashman said of the right-handed hitter, who is playing for Scranton/Wilkes-Barre on a rehab assignment. “If he is rusty, he keeps going. If he doesn’t look rusty, we will take him. We have to get him to play nine innings of defense and go from there. It could happen before the All-Star break.’’

Thames has been on the DL with a right hamstring problem since June 13.

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Alfredo Aceves threw a bullpen session in Tampa, and Sergio Mitre was slated to toss an inning for Tampa (Single-A).