5G equipment made by the Chinese firm is currently subject to security concerns amid accusations of links to the Chinese government, which the company has denied.
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 – though a temporary licence that eased restrictions was recently extended to November.
“I would hope that we can 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 that 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.”
Earlier this month, Huawei’s founder, Ren Zhengfei, said he does not believe the UK will exclude the firm, saying: “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 Science and Technology Select Committee said there are no technological grounds for banning Huawei in a report published in July but said some ethical concerns remain.
Meanwhile, Dominic Grieve’s Intelligence and Security Committee has called for conclusion “as a matter of priority” for Prime Minister Boris Johnson, warning that the extent of the delay is “damaging the UK’s international relationships”.