His comments would appear to contradict a statement by US Homeland Secretary Tom Ridge made in July. Back then he said US intelligence showed the al-Qaida network was planning a "large-scale attack in the United States in an effort to disrupt our democratic process".
At the same time, Ridge had said "we lack precise knowledge about time, place and method of attack".
However on a Fox News Channel exchange recorded on Saturday while campaigning in Florida, Bush said: "I don't want to alarm anybody because I don't, I just, there's nothing specific at this point in time, (only) a kind of general intent.
"They do think about whether or not they can try to disrupt our elections. We have no actionable intelligence."
The president also said he was not sure whether the "war on terrorism" he declared after the 11 September 2001 attacks would ever completely stamp out "extremist" violence, saying that was "up in the air".
"America is safer under the course of action we've taken, but not yet safe. Whether or not we can be ever fully safe is up, you know, is up in the air," said Bush, who drew fire in August when he said the war might not be winnable.
Democratic White House hopeful John Kerry used an NBC television interview to criticise Bush for saying then "I don't think you can win it. But I think you can create conditions so that those who use terror as a tool are less acceptable in parts of the world."