The US national security advisor has claimed he was told on his trip to the country that government officials are planning to reevaluate the situation, following the appointment of Prime Minister Boris Johnson.
US President Donald Trump recently added the Chinese firm to a list of companies that US firms cannot trade with unless they have a license, amid the fears of national security concerns.
But Huawei have repeatedly denied allegations that the use of their products presents security risks, and said it is independent from the Chinese government.
According to the Financial Times newspaper, Bolton said: "They were very concerned about not having any compromise in security of telecommunications in the 5G space.
"What they said was 'we would like to review this and be very sure about our decision and we too are concerned about the security of our 5G telecommunications network'."
Trump recently revealed he will allow US business to "sell Huawei equipment" which has "no great national security problem with it".
He said: "US companies can sell their equipment to Huawei.
"We're talking about equipment where there's no great national security problem with it.
"I said that's okay, that we will keep selling that product, these are American companies that make these products.
"I've agreed to allow them to continue to sell that product so that American companies will continue."