Gavin Williamson's comments - reported by the Times - came after some nations restricted use of the firm's products in 5G networks over security concerns.
MI6's head recently said Britain faced decisions on Chinese ownership of tech.
The UK says China is behind hackers targeting commercial secrets. Huawei denies any link to the Chinese state.
On Wednesday, Mr Williamson was reported as saying: "I have grave, very deep concerns about Huawei providing the 5G network in Britain. It's something we'd have to look at very closely."
Australia, New Zealand and the US have restricted use of Huawei technology in 5G mobile networks, and Mr Williamson said the UK would look at their example.
"We've got to recognise the fact, as has been recently exposed, that the Chinese state does sometimes act in a malign way," he added.
