The Home Office has not ruled out an amnesty for illegal immigrants, despite previously denying one would go ahead.
Home Office minister Liam Byrne said it is too early to tell whether he will allow the controversial move, adding he wants more information before he makes a decision.
Estimates put the number of people living in Britain without permission at about 500,000.
Labour has been considering the idea for at least three years. Former Home Secretary David Blunkett said it was mooted when he was heading the department.
And Jack Dromey, deputy general secretary of the Transport and General Workers Union, welcomed the possibility of an amnesty.
He said: "The time has come for the Government to be brave, distinguishing between deporting the few who commit serious crimes and allowing the many undocumented migrant workers to remain."
He said: "They are good men and women, essential to our economy and pillars of their local churches and communities."