The radical cleric was finally deported from the UK last July after a near decade long battle that cost around £2m.
However, he was acquitted yesterday of conspiring to commit acts of terrorism, according to reports in the country.
Qatada is still facing separate charges at the state security court in capital Amman relating to a terror plot in Jordan.
Asked if David Cameron would welcome him back if cleared, the Prime Minister’s spokesman said: “He can’t come back, and he won’t come back.
“He is a Jordanian and he does not have a UK passport.
“He would not be granted permission to enter the UK, end of story.”
Once dubbed Osama bin Laden’s right-hand man in Europe, Qatada arrived in Britain on a forged passport in 1993 after fleeing a Jordanian government crackdown on militants. He was granted asylum in the UK a year later.
Efforts to remove the father of five to Jordan to stand trial for alleged terrorist activities were repeatedly thwarted under human rights laws, until the state gave formal assurances that evidence obtained through torture would not be used against him.
The PM’s spokesman said: “This is a man who the British courts have deemed a risk to national security...
“You saw the outcome, the very successful outcome, of all the work the Home Secretary and her team did when Mr Qatada was put on a plane to Jordan, and he is not coming back.”
Deputy Prime Minister Nick Clegg told LBC: “What is absolutely clear to me is this man needed to face justice and needed to do so out of the United Kingdom and that’s what this government finally achieved...
“We don’t want this man back.”
Home Affairs committee chairman Keith Vaz said: “I am surprised at this verdict. However, it is right that the Jordanian court has followed due process.
“There are still matters outstanding which need to be resolved.
“The British Government was right to remove this man from the UK considering his extremist views and potential links to terrorism.
“We must continue to support the Jordanian Government.”