Both quoted a government source as saying he would be granted a one-year temporary resident permit.
Black's release from the Miami-area prison could come as early as Friday, the Canadian Broadcasting Corp. reported.
He is serving time for a U.S. conviction for fraud and obstruction of justice related to his tenure as chairman and chief executive officer of Hollinger International Inc. The company operated a raft of newspapers in Britain, Canada, Israel and the United States. Black and others were accused of bilking investors of about $60 million.
In 2001, the Montreal-born Black changed his Canadian citizenship to British in order to secure a peerage in the House of Lords. However, he maintained a mansion in Toronto, where his wife lives, on a temporary resident permit.
Normally, non-Canadians with criminal convictions are barred from living in the country.
In Parliament, Citizenship and Immigration Minister Jason Kenney said he had nothing to do with the decision and it was in the hands of senior public officials, said the Post, which Black founded.