The tech firm says it will not install a backdoor to provide individuals' information to US authorities
Last week, a court ordered Apple to help the FBI hack into a locked iPhone used by Syed Farook, who together with his wife Tashfeen Malik killed 14 people in San Bernardino, California, in December.
Apple opposes the order, arguing such a move would violate its free speech rights and override the will of Congress.
Google now plans to file a "friend of the court" brief on Apple's behalf within the next week, according to a source familiar with the situation.
Like Apple, it fears creating a precedent that authorities could use to read messages, photos and other sensitive information stored on phones.
Apple meanwhile has filed its formal objection in the case.
In its filing, Apple said: "The government's request here creates an unprecedented burden on Apple and violates Apple's First Amendment rights against compelled speech."
Apple also contended that the court was overstepping its jurisdiction, noting that Congress had rejected legislation that would have required companies to do the things the government is asking Apple to do in this case.
"No court has ever authorised what the government now seeks, no law supports such unlimited and sweeping use of the judicial process, and the Constitution forbids it," Apple said.
The government argues that the All Writs Act, a broad 1789 law which enables judges to require actions necessary to enforce their own orders, compels Apple to comply with its request.
Just days ago Microsoft founder Bill Gates waded into the row and surprisingly sided with the FBI.
He said: "This is a specific case where the government is asking for access to information. They are not asking for some general thing, they are asking for a particular case."
The New York Times reports that Apple has begun developing a security update for its devices which would make it impossible to install the kind of backdoor which the FBI has requested.
Tim Cook has argued that creating backdoors in encrypted networks creates a backdoor for "everyone." He said that accessing user information would "undermine the very freedoms and liberty our government is meant to protect."