Yankees co-chairman Hank Steinbrenner said the reports would not faze the club.
"It's no distraction to the team," Steinbrenner said Thursday at the Yankees' complex in Tampa, Fla. "Whether it is to Alex I don't know. But from what I'm hearing, no, it's not."
Coverage of the private lives of Yankees is not new, particularly in an era in which professional athletes are increasingly scrutinized off the field.
Earlier this year, it was reported that former Yankee pitcher Roger Clemens had an affair with country music singer Mindy McCready. Derek Jeter's string of girlfriends also have received considerable press, most notably a relationship with another mega-selling singer, Mariah Carey.
Rodriguez, however, has found himself in the tabloids more than any other Yankee since arriving in New York in 2004. Last year, he was labeled "Stray-Rod" on the front page of the New York Post after being photographed out at night with a former Vegas stripper.
"I think for Alex, he's been through this before, he knows how to handle it," Yankees manager Joe Girardi said. "I'm sure there are times he wishes he could just fit in. That's the price you pay."
"Obviously, everyone likes to keep their life private. Unfortunately, in this world, that doesn't happen."
A copy of a local tabloid with a front-cover headline of "Split!" was on a table in the middle of the Boston clubhouse.
"New York, it's like Us Weekly meets the fun bunch," Red Sox first baseman Sean Casey said.
On Thursday, sports talk radio in New York was dominated by larger concerns: mainly the dim playoff prospects for both the Yankees and Mets.
The sports blog Deadspin wondered Thursday how Rodriguez would be greeted by fans at Yankee Stadium in the team's upcoming series against the Red Sox: "Will there be any cone bras in the stands? Sean Penn masks? The theme from `Evita' being sung by a heavenly choir of visiting Red Sox fans?"
There were, as usual, a lot of fans wearing pinstripe jerseys with his No. 13 on the back for the series opener. One of them, Shawn Richards, said he and nine pals came from western Canada to cheer for Rodriguez.
"A-Rod's the man!" Richards said. "He can do whatever he wants. It's New York."