Joe Girardi spoke for 10 minutes and Brian Cashman for more than 20, but in no part of their trade-deadline postmortem Monday did either truly clarify one of the Yankees’ biggest mysteries: What are they going to do with Alex Rodriguez?

Rodriguez, 41, has been struggling, and with one year left on his contract, it’s not readily apparent how he’ll fit into the Yankees’ rebuild. With the team keen on trying out some of its young talent, it even seems possible that he could find himself without any role at all.

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“A-Rod is a choice for manager and coaching staff as they try to dissect every day,” Cashman said, making it clear that he will not automatically inherit the everyday DH role after the Carlos Beltran trade. “He’s going to do everything he continues to do to try to put himself in a position to succeed and then leave the decision-making to the field staff if there’s opportunities to play or not.”

Rodriguez, who wasn’t in the lineup Monday night in the National League park, is four home runs shy of 700 and is hitting .205 in 61 games this year. He has four hits in his last 35 at-bats.

At this point, it seems possible that the Yankees will buy him out, and Girardi momentarily helped lend to that speculation when he said he wasn’t “sure there won’t be other things done over the course of this week.”

When asked if he was alluding to Rodriguez, he said, “That’s not what I meant. As we move forward, we’ll judge the at-bats at DH and we’ll put what we feel is the best opportunity for us to win.”