Mr Zaidi's attack was launched with the words "this is a farewell kiss, you dog"
The Iraqi journalist who hurled his shoes at US President George W Bush is seeking asylum in Switzerland, Swiss newspaper Tribune de Geneve reports.
Muntadar al-Zaidi has been in custody in Iraq awaiting trial since the incident during a visit by Mr Bush to the country in mid-December.
He fears for his safety in his Baghdad prison, the paper says, quoting his lawyer, Mauro Poggia.
The lawyer argues his client likewise cannot resume his old job in Iraq.
Since his arrest, the Iraqi has reportedly been beaten in custody, suffering a broken arm, broken ribs and internal bleeding, his older brother Dargham told the BBC last month.
Mr Zaidi said he was acting to avenge Iraqi widows and orphans
Mr Zaidi, 29, launched his news conference attack at the outgoing American president, who led the invasion of Iraq in 2003, with the words "This is a farewell kiss, you dog".
In Arab culture, it is considered rude even to display the sole of one's shoe to a fellow human being, let alone throw it at them.
Mr Poggia said he had been contacted by Mr Zaidi's family and was drafting a letter to the Swiss foreign ministry requesting its assistance in granting him political asylum.
"Even if many Iraqis support his act, he is at the mercy of all kinds of extremists..." he said.
"His life could become hell in his own country."
In Geneva, by contrast, "this single man who has no children may very well work as a journalist at the United Nations", the lawyer told the Tribune de Geneve.
The trial of Mr Zaidi, who reportedly remains unrepentant, was postponed at the end of December amid discussion about whether he should be charged with either assaulting or insulting Mr Bush.