Terry Jones sparked condemnation around the world when he threatened to burn the Koran on the anniversary of the 9/11 terror attacks.
He intends to preach "against the evils and destructiveness of Islam" at an English Defence League (EDL) rally in Luton, Bedfordshire, on February 5.
Mrs May told Sky News' Sunday Live: "Of course the Home Secretary has the right to exclude people who are not conducive to public good or on national security grounds.
"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 coming to the UK, then of course this is a case that I will be actively looking at."
A statement on the pastor's website said: "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."
Anti-extremist group Hope not Hate condemned the move and launched a petition calling for Mr Jones to be banned from the UK.
Its 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.
"It is yet another example of how the EDL exists only to sow the seeds of intimidation and division."
Weyman Bennett, joint national secretary of Unite Against Fascism, accused Mr Jones of coming to Britain to "whip up Islamophobia and racism".
He said: "We intend on calling a mass demonstration where everyone can oppose the growth of racism and fascism in this country."