The Miami New Times reported late last month that the three-time AL MVP bought human growth hormone and other performance-enhancing substances in recent years from Biogenesis of America LLC, a now-closed clinic in Coral Cables, near Rodriguez's offseason home.
Speaking on Friday at the Yankees' minor league complex, Steinbrenner said the situation is "a concern, but it's out of our hands."
"We will cooperate with MLB in any way we can, any way we're asked to," he said. "But other than that, there's not much to say. I don't know any more than you do."
Rodriguez has denied the allegations. He admitted four years ago that he used PEDs from 2001-03.
The Yankees signed one-time Boston Red Sox third baseman Kevin Youkilis to fill in for Rodriguez, who is sidelined for at least the first half of the season after hip surgery Jan. 16.
"I've always liked Kevin," Steinbrenner said. "He always seemed like a good leader, a hard worker and a very enthusiastic—loves the game—kind of guy. And that's the kind of guy we want."
Steinbrenner addressed a number of other topics, including the contract status of second baseman Robinson Cano, a potential free agent after the upcoming season.
"There's been a conversation or two," Steinbrenner said. "We'll get into that, and we'll talk about that at a later date. But he's obviously been a great Yankee, and hope he's here his entire career."
Steinbrenner feels the Yankees have a "championship-caliber team" this season. He acknowledged the club is sometimes criticized for fielding an older roster, but he likes its experience, "assuming we can stay away from injuries."
"We've got a lot of good veterans on the team, and we've got some good young players as well," Steinbrenner said. "That's always the mix that I want to shoot for. I like our team, but where we end up in October, anybody's guess."
The Yankees are still looking to reduce the 2014 payroll to the $189 million luxury tax threshold.
"All I can assure the fans is, we're always going to field a championship-caliber team every single year," Steinbrenner said. "Is that our goal next year? Yes, to be at that number, that's our goal. But as I've said from the beginning, it depends on some of our young players stepping up and getting the job done. That has to happen, or it's going to be difficult."
The Yankees re-signed a number of their own free agents, including pitchers Mariano Rivera, Andy Pettitte and Hiroki Kuroda, but were less active than many previous years for outside free agents.
"I think we have some good signings, and I think we did our fair share in the offseason," Steinbrenner said. "Similar payroll to last year. Shows we want to win."