The UK is considering the inclusion of Huawei equipment in the project after US president Donald Trump in May effectively banned the company from trading with American firms.
Concerns have been expressed about the security of Huawei’s 5G equipment and its alleged links to the Chinese government.
Huawei’s Ren Zhengfei told Sky News that Britain had a “very important” decision to make about the rollout.
He added: “I think they won’t say no to us as long as they go through those rigorous tests and look at it in a serious manner and I think if they do say no, it won’t be to us.”
The UK’s National Security Council decided in April to an in-principle block against Huawei accessing critical parts of national networks.
Last month, then culture secretary Jeremy Wright said the UK was still seeking clarity on the implications of US action against the Chinese firm, adding it would be “wrong to make specific decisions” before this had been achieved.
The White House said Mr Trump and Prime Minister Boris Johnson discussed issues including “trade, 5G and global security” in their latest phone call earlier this month.
The debate over Huawei’s future in the UK as a provider of 5G telecoms equipment has been a lingering issue, amid fears that it could enable the Chinese government to spy on people in the West – an allegation the firm has repeatedly denied.
In an indication of easing over Huawei, Three and Sky Mobile recently said they would offer the firm’s 5G smartphone to customers as part of the rollout of their new 5G mobile networks, making them the first UK mobile operators to do so.
Last week, US national security adviser John Bolton said during a visit to the UK that fears over Huawei’s involvement in Britain’s 5G network could wait until after Brexit to be resolved.
He said representatives of Mr Johnson’s government had expressed an appreciation for the White House’s views on Huawei.
He added: “They said in particular that looking really from square one on the Huawei issue that they were very concerned about not having any compromise in the security of telecommunications in the 5G space.”