The Canadian government says a brother-in-law of the ousted Tunisian president has applied for refugee status.
Foreign Minister Lawrence Cannon had earlier suggested Canada would comply with a request for the extradition of Belhassen Trabelsi.
The billionaire businessman fled to Canada last week after President Zine al-Abidine Ben Ali was ousted.
Mr Cannon says the government has to abide by the law so Mr Trabelsi has the right to take his asylum case to court.
Correspondents say that under Canadian law, dealing with such an application could take years.
The Tunisian tycoon had permanent residency status in Canada and reportedly flew into Montreal by private jet last week with his wife, four children and a nanny.
His status is reported to have been revoked since then and the government in Ottawa has also moved to seize his Canadian assets.
"We have indicated that these people are not welcome in Canada," Mr Cannon told the Canadian Broadcasting Corporation on Saturday, "but obviously, that having been stated, Canada is nonetheless a country that has legislation, we do abide by the rule of law."
The foreign minister said authorities are in contact with Mr Trabelsi's lawyer in Montreal.
It is not known exactly where Mr Trabelsi and his family are at the moment.
They were believed to be staying at the Chateau Vaudreuil Suites Hotel in Montreal but are thought to have left on Thursday.
Belhassen is the oldest brother of Leila Trabelsi, a former hairdresser who became the first lady of Tunisia.
She fled with Mr Ben Ali to Saudi Arabia after a series of protests against poverty and corruption in Tunisia put an end to his 23 years of rule.
Mr Trabelsi has been accused by the transitional Tunisian government of property theft and illegal transfer of foreign currency, among other charges.
His presence in Canada has angered many Tunisian expatriates.