If they are looking for clues they might as well ask local shop keeper Salah Mahmud.
"He is everywhere. When nobody was looking for him, he changed his location every two days," said Mahmud, who runs a photo shop on Saddam Street. "So nowadays, he is changing three or four times a day."
Five months after capturing Baghdad, US officials do not hide their frustration at their failure to find Saddam Hussein, who has a 25-million-dollar bounty on his head.
The last confirmed sighting of Saddam Hussein was on 9 April, shortly before the first US troops entered Baghdad and ousted him from 24 years in power. The massive manhunt has since led down one blind alley after another.
Qusay (L) and Uday's deaths did not
result in finding of Saddam Hussein
The arrest of several top aides fuelled speculation that the US was closing in on him. It reached a feverish pitch after US forces killed his sons, Uday and Qusay, in a raid on a villa in Mosul on 22 July.
Ten days ago US troops, backed by helicopters, moved into a neighbourhood of the northern city of Mosul after intelligence reports said he might be hiding there.
But again the search proved fruitless.
US commanders have stepped up their effort to penetrate the world of the fugitive leader, even recruiting some of his former intelligence agents, according to Ali Abdul Amir, spokesman for the pro-US Iraqi National Accord.
Wafiq al-Samarrai, a former Iraqi dissident and one-time chief of Iraqi military intelligence before falling out with Saddam, said the US would eventually succeed in arresting his old boss, perhaps in a matter of weeks.
"Especially if he continues to try and send messages. From my personal point of view I have the impression that he is in Baghdad, Samarrai said. "It's hard to believe he is still hiding while there is a price on his head," he said.
But even Samarrai is perplexed at the failure of the occupation forces to nab Saddam Hussein after offering such a sizeable reward for information leading to his arrest.
"He is protected by Arab mercenaries from Syria, Palestine, Lebanon and Jordan because he can't trust the people from Iraq anymore"
Conspiracy theories on what happened to the once all-powerful leader provide lively banter in the street cafes of this occupied country.
Near Mahmud's photo shop a group of men and women are convinced Saddam Hussein is receiving help from outside forces.
"He is protected by Arab mercenaries from Syria, Palestine, Lebanon and Jordan because he can't trust the people from Iraq anymore," speculated Fatma al-Zuru.
She said it was impossible to believe that the Americans did not know where he was hiding. "They brought Saddam to power and surely they have found him and now they are protecting him," Zuru added.
In Al-Adhamiya, a Sunni neighbourhood, old men playing cards inside a coffee shop point to the deaths of Saddam's prized sons as the main argument to support theories he was no longer in the country.
"If he stayed inside the country, he would have reacted after Qusay's and Uday's death," said one.