Digital Secretary Nicky Morgan told the BBC she hoped the government "could do something by the autumn".
She stressed that the UK needed to make the "right decision" to help keep its networks secure.
In June, China warned the UK that excluding Huawei from its 5G network "sends a very bad signal".
"I would hope that we could do something by the autumn, but we want to make the right decision and we've got to make sure that this is going to be a decision for the long term, making sure we keep all our networks secure," Ms Morgan told BBC Radio 4's Today programme.
"Huawei are not involved in the provision of government networks at the moment and that's absolutely going to stay the same way, but we will look at all circumstances."
Huawei told the the BBC that it welcomed Ms Morgan's "commitment" to "world-class digital infrastructure".
"Over the last 18 years, we have helped build the UK's broadband, 3G and 4G networks and, as independent analysts agree, Huawei can help British operators develop 5G networks that are more secure, more affordable and completed more quickly - helping to keep bills down for consumers and connect rural areas," a spokesman said.
On Sunday, Prime Minister Boris Johnson and President Donald Trump discussed 5G and Huawei at a meeting during the G7 Summit in Biarritz, France.