Terry Jones has been invited to an English Defence League (EDL) rally to speak out "against the evils and destructiveness of Islam".
The Florida-based pastor caused a domestic and international firestorm earlier this year after threatening to torch hundreds of Qurans -- the holy book of Islam -- to mark the anniversary of the 11 September 2001 attacks.
The EDL has emerged in the past couple of years to fight against what it says is the spread of militant Islam in Britain.
Jones' website says he intends to visit an EDL rally on 5 February in Luton, a town north of London which has a significant Muslim minority.
"During the protest, Dr 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.
May has the power to exclude or deport an individual if she thinks their presence in Britain could threaten public order or national security.
"Of course the home secretary has the right to exclude people who are not conducive to public good or on national security grounds," she told Sky News television.
"Pastor Terry Jones has been on my radar for a few months now.
"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."
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 added.
Anti-racism campaigners deplored the idea of such a visit. Hope Not Hate director Nick Lowles said: "Pastor Jones should not be allowed to set foot in the United Kingdom. Only extremists will benefit from his visit and, as we know, extremism breeds hatred and hatred breeds violence."
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.