Lee also said he has already been talking to companies working on the Government's ultra-fast broadband scheme as well as those involved with Australia's National Broadband Network.
The Chinese companies entrance into the market could put a spanner the works of Pacific Fibre, the local firm planning an internet cable between New Zealand, Australia and the United States.
Pacific Fibre has made strong gains in gathering funds for the build and signed a number of long-term contracts this year, including a $100 million deal with Vodafone.
The company has also been courting Chinese investors, following a New Zealand information and communications technology trade delegation to Shanghai and Hangzhou last month which met operators such as China Mobile and China Telecom.
If work gets underway on the US$400 million project, Pacific Fibre's 12,000 km cable is due to be operational by the first quarter of 2014.
The announcement from Axin and Huawei may also cause issues for Kordia's trans-tasman cable, Optikor.
The state-owned transmission company first announced its intentions to build the transtasman internet pipe in 2008, but has struggled to gather funds to do so.
Kordia said this month its "OptiKor" cable was on hold.
"Our assessment is that the market isn't quite ready (for the cable). We've done the work, we're taking a pause at present, there are other cable projects around. When the market conditions change we'll reignite," Kordia chief executive Geoff Hunt said.
The Southern Cross Cable Network currently operates the only internet link out of New Zealand and its rivals argue a second player would bring competition to the market and put downward pressure on the price of international capacity.