Jones had planned to speak at an English Defence League (EDL) rally in Luton, Bedfordhsire on February 5.
"Of course the home secretary has the right to exclude people who are not conducive to public good or on national security grounds,” Home Secretary Theresa May told Sky News
"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, who leads a small church in Florida, had earlier told Sky
that he is not against Muslims, but is against “Sharia law and Muslims not willing to submit to the constitution."
quoted EDL leader Tommy Robinson as saying: "Pastor Terry Jones contacted me personally to ask if he could attend our demonstration."
"He wants to speak about the evils of Islam at the protest. It is a medieval religion."
Jones told the BBC
that he planned to speak against "radical Islam", not "all Islam."
"We have no problem with Muslims - we have freedom of speech and religion - Muslims who want to make our country their country, obey our laws and constitution,” he said.
"We have a problem with them, which I believe you all have also, when they go on the street... and they call for the death of the UK, for the death of Israel, for the death of America. They call for Sharia law.
"They say they are going to turn Buckingham Palace into a mosque and the Queen must convert to Islam or leave the country."
Campaigners are calling for him to be banned from Britain. The group Hope Not Hate has launched campaign urging May to ban him.
Campaign co-ordinator Nick Lowles said that Jones indiscriminately targets all Muslims.
reported that George Readings, spokesman for counter-extremism think tank, Quilliam, said: "The EDL has only invited him here to stir up trouble."
The Stand Up America
website states that Jones plans to “speak against the evils and destructiveness of Islam in support of the continued fight against the Islamification of England and Europe."
reported that the May has the authority to exclude or deport Jones if his presence in the UK is a threat to national security, public order or the safety of citizens, or if she feels his views glorify terrorism, promote violence or encourage other serious crime.
Her decision could be reversed though. Dutch politician Geert Wilders was banned by the Home Office last year, but that decision was overturned at an immigration tribunal.