The Times report said the sources, described as people within baseball who were briefed on the matter, requested anonymity because they did not want to be identified discussing an ongoing investigation.
Yankees manager Joe Girardi, general manager Brian Cashman and captain Derek Jeter all said they had not been contacted by MLB and were not aware of any investigation.
"I'm sure if there was a problem before, we would have been contacted," Girardi said. "That's my thought. We are going to move on from this. People can talk about it, but we're going to move on."
"I only worry about things that are in my control," Cashman said. "I really have no comment about whether there is or isn't [an investigation]. That's really a question for Major League Baseball."
The report of an ongoing investigation by MLB comes while Rodriguez is working out in Tampa, Fla., preparing to return from hip surgery, possibly as soon as next weekend.
In addition, the book "A-Rod: The Many Lives of Alex Rodriguez," by Sports Illustrated senior writer Selena Roberts, is due out Monday, and it reportedly includes allegations that Rodriguez used steroids while with the Yankees and in high school.
When it hits bookstore shelves, don't expect Girardi to be among those in line to purchase it. Girardi delivered an impassioned defense of Rodriguez to reporters in a news conference before Sunday's scheduled game against the Angels at Yankee Stadium.
"I don't want Alex to be a target," Girardi said. "I have some issues with it. It's interesting how the book date got moved up now. I get tired of answering these questions. It's just -- I don't understand why someone would write a book like this anyway. Some people may not care to hear that, but I don't understand it. ... I don't necessarily know why it has to be put in a book, unless the person volunteers it. It's something I've never understood."
Girardi said that he has read excerpts of the book published in newspaper accounts, which also contains explicit details about Rodriguez's off-the-field life.
"I think sometimes things are written about that none of us are proud of," Girardi said. "There's things in my life that I'm not proud of that I've done. I wouldn't want my kids to have to deal with that. I tell my kids that daddy makes mistakes, I do, and I apologize for them. I say, 'Daddy's not perfect.' But it's not necessarily something that I would want them to read about all the time and be the focus. This man wants to be a father, too."
Cashman said that he had not heard Girardi's comments but understood his position if he was defending his player.
"I think Joe is just expressing the fact that this is a member of our family and making sure that people know," Cashman said. "He sat next to him in Spring Training, as did I, and Alex answered a lot of the questions. I'm sure there will be more questions that will be asked, and when they need to be answered, that's up to Alex. I just think that at some point, we'll try to move on as best we can."
Rodriguez probably won't have to answer many inquiries from his Yankees teammates, who have largely said that they have little interest in the book's upcoming release.
"We're a team in here, so we're going to focus on baseball right now," Joba Chamberlain said. "That's what we've got to do."
"It gets a little tiring," said Phil Hughes, who added, "I haven't read a book since high school."
According to the Times, investigators who met with Rodriguez on March 1 in Tampa had questions about the consistency of his statements to them, and they launched further investigations shortly thereafter.
At that meeting, Rodriguez maintained his use was in 2001-03, that he'd received it from his cousin, Yuri Sucart, and that he did not receive illegal substances from banned trainer Angel Presinal.
The newspaper also reported that an investigator on Friday asked Roberts if she would cooperate with baseball's inquiry.
"I said that as a journalist, I cover MLB, and cooperating with them on this would be a conflict of interest, and he said that he understood the position that I am in," Roberts told the newspaper in a telephone interview.