Shanahan said Thursday that he will speak to Moss "at the right time" about the matter and has not been contacted by the league.
"Let's just wait and see before we throw him underneath the bus," Shanahan said after speaking at a local Chamber of Commerce luncheon.
The Buffalo News and Washington Post reported that Moss has received treatment from Galea and is the unidentified Washington player mentioned in an affidavit associated with the case. The affidavit said the Washington player was planning to meet with Galea at a hotel last September.
The Washington Post earlier reported that Moss received human growth hormone from Galea but has since changed its report to say that Moss received only treatment from the doctor.
"Just because he's been associated with a doctor doesn't mean this person's guilty," Shanahan said.
Shanahan said he's talked to "a couple of people" whose names have been associated previously with Galea.
"A lot of people whose names have been associated, there's no repercussions," the coach said. "So we're getting a little ahead of ourselves right now."
Galea is accused of smuggling, unlawful distribution of human growth hormone and unlawfully treating professional athletes. On Wednesday, a Canadian court document revealed that Galea made multiple trips to New York City, Boston, Cleveland and other U.S. cities to meet with professional athletes.
Moss is not in danger of being charged in the case, however. He had no comment Thursday and declined ESPN's request for interview through his representatives.
The Redskins also declined to comment Thursday when contacted by ESPN.
"At this juncture, any of the persons who are alleged to have used these substances are considered witnesses, and not targets, of this investigation," William J. Hochul Jr., the U.S. attorney in Buffalo, told The Buffalo News.
Mark J. Mahoney, one of Galea's attorneys, said his client did nothing wrong.
"Officials of the NFL and other sports organizations can sleep soundly tonight, because there is nothing he did with these athletes to help them with performance enhancement," Mahoney told The Buffalo News on Wednesday.
"[Galea] strictly provided treatment for injuries. If any athlete got [HGH], it was injected directly into injured tissue, in very small amounts, for purposes of healing," Mahoney told the newspaper.
When contacted Wednesday by The Washington Post about allegations involving an unnamed Redskins player, Moss tried to keep the topic on football.
"I'll talk about football. I don't know about nothing else," Moss told the newspaper. "I ain't got nothing to do with nothing that ain't about me."
Moss has played five seasons with the Redskins and previously spent four years with the New York Jets. He revealed at minicamp earlier this month that he recently had arthroscopic knee surgery on his left knee to fix a problem that had been bothering him for three years.
"Santana's been out for a while," Shanahan said. "He's been working extremely hard over at the facility. We understand the rules and the guidelines and they're very explicit, so hopefully we do things the right way."
Moss would likely be suspended by the NFL if he is found to have taken human growth hormone or any other banned substance.
"I treat it like a sprained ankle," Shanahan said. "If a player broke their ankle and they're gone for the year, they're gone for the year."
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