The NSA accessed Huawei's email archive, communication between top company officials internal documents, and even the secret source code of individual Huawei products, said the reports, based on documents provided by fugitive NSA contractor Edward Snowden.
"We currently have good access and so much data that we don't know what to do with it," states one internal document cited by Der Spiegel on Saturday.
Huawei — founded in 1987 by former People's Liberation Army engineer Ren Zhengfei — has long been seen by Washington as a potential security Trojan Horse due to perceived close links to the Chinese government, which it denies.
The US and Australia have barred Huawei from involvement in broadband projects over espionage fears.
Shenzhen-based Huawei is one of the world's leading network equipment providers and is the world's third-largest smartphone vendor.
The original goal of Operation "Shotgiant" was to find links between Huawei and the Chinese military, according to a 2010 document cited by The Times.
But it then expanded with the goal of learning how to penetrate Huawei computer and telephone networks sold to third countries.
"Many of our targets communicate over Huawei-produced products," the NSA document read, according to The Times.
"We want to make sure that we know how to exploit these products," it added, to "gain access to networks of interest" around the world.
Huawei is a major competitor to US-based Cisco Systems Inc — but US officials insist that the spy agencies are not waging an industrial espionage campaign on behalf of US companies, as Snowden has alleged.
"The fact that we target foreign companies for intelligence is not part of any economic espionage," a senior intelligence official told reporters Thursday.
The goal of economic intelligence efforts is "to support national security interests," and "not to try to help Boeing," the official said.