Speaking with reporters at George M. Steinbrenner Field, Rodriguez said he had "nothing new to report" regarding a potential meeting with investigators, who have expressed an interest in speaking to him regarding Galea.
"I'm at ease no matter what," Rodriguez said.
The Associated Press reported Monday that Galea said he treated Rodriguez following his hip surgery last year, but provided him only with anti-inflammatories.
When asked if Rodriguez was keeping quiet because he wanted to or because he had been instructed to, he responded, "I think the latter."
Galea faces charges in Canada and the United States of illegally importing banned performance-enhancing substances. He has reportedly treated many professional athletes over the years, including golf superstar Tiger Woods and Olympic swimmer Dara Torres.
Galea maintained in the AP report that he has never given human growth hormone to any athlete.
Federal authorities have cast a wide net in their search for information regarding the doctor, and Rodriguez is one of the professional athletes who have been contacted by authorities recently about the doctor.
Mets players Jose Reyes and Carlos Beltran have also been questioned by authorities. Rodriguez said that he had not spoken to either player about the investigation.
Reyes said this spring that he had been interviewed by federal authorities about his connection to Galea and now considered his role complete. The shortstop said he went to Galea for a medical process called "blood spinning," which Galea is said to have developed, in an attempt to accelerate the healing in his right hamstring.
Beltran said after his interview with the authorities that he received treatment from Galea for a bone bruise behind his right kneecap, but he denied having any injections.
Colorado hurler Huston Street, treated by Galea for an elbow injury in 2007 and a hip injury in '08, has also been informed he could be called upon for questioning.
"I was notified by my agents that I may or may not be asked questions, whether that's from the U.S. attorney's office or the Commissioner's Office," Street said. "I really don't know the specifics of why he is in trouble, why he is not in trouble. I know that everything we had talked about ... that we were going to do procedurally, was 100 percent within the law. We went to him because he's been very good with getting injuries healed."
The investigation has been spearheaded by agents from Buffalo, N.Y., where one of Galea's assistants was caught transporting HGH across the border from Canada. Galea faces charges relating to the illegal smuggling of HGH and the distribution and sale of the illegal drug Actovegin. Actovegin, which is deprotenized extract of calf blood, reportedly has valid medical uses, but it is be viewed as a potential performance-enhancing drug.
When asked by reporters about his role in the investigation last week, Rodriguez expressed his desire to cooperate fully.
"I am aware of an investigation, and I plan on cooperating," Rodriguez said.
For their part, the Yankees released the following statement last week about their star third baseman's involvement with Galea:
"The New York Yankees have not been contacted with regard to an investigation of Dr. Tony Galea. The Yankees never authorized Dr. Tony Galea to treat Alex Rodriguez, nor do we have any knowledge of any such treatment.
"The Yankees authorized Dr. Marc Philippon to operate on Alex and oversee his rehabilitation. At the request of Dr. Philippon, we also authorized Dr. Mark Lindsay to supervise the daily rehabilitation program established by Dr. Philippon. We will continue to monitor the situation."
Bryan Hoch is a reporter for MLB.com. Bailey Stephens contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.