US pastor Terry Jones said in his website that he had been invited to address a rally in February, organised by English Defence League (EDL), a far-right group, about "the evils and destructiveness of Islam".
Theresa May, Britain's interior minister, said on Sunday she was "actively looking" at the case. She said Jones had "been on her radar for a few months" and, as home secretary, she could ban his entry if he was a threat to national security.
The government has the power to bar people considered a threat to public safety or national security.
"Only extremists will benefit from his visit"
director of Hope Not Hate
"It wasn't clear that he was definitely coming to the UK but if it is now clear that he's definitely coming to the UK, then of course this is a case that I will be actively looking at," May told UK's Sky News television.
The EDL has emerged in the past couple of years to oppose what it calls the spread of Islam, Sharia law and Islamic extremism in England.
Its opponents say the group is racist and stages violent protests.
Jones' website says he intends to visit an EDL rally on February 5 in Luton, which has a significant Muslim minority.
"During the protest, Terry Jones, will speak against the evils and destructiveness of Islam in support of the continued fight against the Islamification of England and Europe," the website says.
Jones told Sky News he would "respect the laws" of any country he visited.
"I would by no means advocate something, preach something, speak something that will cause that type of riot or disturbance," he said.
A previously obscure preacher, Jones gained infamy through his effort to burn the Quran. He cancelled the event after international pressure.
Anti-racism campaigners deplored the idea of such a visit and say his visit will only breed hatred and violence.
Nick Lowles, the director of the campaigning group Hope Not Hate, said Jones should be barred because "only extremists will benefit from his visit".
Eleven men were arrested by police in Peterborough, eastern England, during an EDL rally on Saturday. About 1,000 people attended the march and another 200 held an opposition rally staged by the local trades union council.