The New York Post reported that Rodriguez chatted with two women after being pinch-hit for in Game 1 of the American League Championship Series, flipping them a baseball to ask for their telephone numbers.
Rodriguez has been benched in Games 3 and 4 of the ALCS, but Cashman said that is because of his struggles against right-handed pitching and not a punitive measure.
"Purely baseball related," Cashman said. "This is all about winning, regardless of the report that is out there that is a non-baseball-related story. It's not going to affect our decision making about who is best to put us in the position to win on a daily basis."
Manager Joe Girardi said he did not know about Rodriguez's actions during Game 1.
"I was not aware of any incident, or alleged incident, or whatever people want to say," Girardi said.
Rodriguez went 0-for-3 in the Game 1 loss to the Tigers and right-hander Doug Fister before being replaced by Eric Chavez as a pinch-hitter in the eighth inning. According to the Post report, Rodriguez stopped chatting with the women only when Derek Jeter fractured his left ankle on a 12th-inning play.
"I addressed that [story] yesterday -- I said it was laughable," Rodriguez said on Wednesday. "I've been here a long time in New York, I think nine years. I've never addressed anything from Page 6. I've never addressed anything from blogs or gossip columns.
"We're here to cover baseball. Some of the criticism out there is very fair and I can live with that, but some of the other stuff is not fair. And you just move on. You don't worry about it too much. I've been in New York a long time."