Ms Rudd also denied that the Government's target to bring migration down to the hundreds of thousands had fuelled the problem.
Ms Rudd will appear before the Home Affairs Select Committee from 3.30pm.
But she admitted her department still had no idea how many migrants have been wrongly detained by immigration authorities - like the grandmother Paulette Wilson, who spent a week in detention after being told she was in Britain illegally.
"The problem", says Stephen Bush in the New Statesman, "is that she can't blame her predecessor [Theresa May] and for one reason or another she won't be calling for either of the things that could resolve the scandal: an ID card scheme, which is unacceptable to many Conservatives and simply wouldn't pass Parliament, or the unpicking of the hostile environment policy which represents the major legislative accomplishment of Theresa May's time at the Home Office and the only legislative accomplishment of May's time at Downing Street".
In April 2016, the then Foreign Secretary Philip Hammond - who is now the chancellor - was told by Caribbean ministers about immigrants facing deportation despite having lived in the United Kingdom for most of their lives, and the BBC understands a report about their concerns was passed to the Home Office, which was led at the time by Mrs May.
The Prime Minister appeared in denial about her role while the Opposition leader does not understand public concerns about illegal immigration.
The Home Office has been hit by more confusion about its immigration policy after a row over deportation "targets".
Asked why it took her so long after repeated media requests from reporters, the Home Secretary said: "We get a lot of journalists, newspapers and MPs giving us their advice".
Amber Rudd, who has faced calls to resign over the crisis, claimed she only became aware there was a "potential issue" over the "past few months".
"If there are removals targets in the Home Office and the two people who supposedly in charge don't know about them, that feels pretty serious", she said.
Long-term residents who arrived in the decades after the Second World War have had their immigration status challenged despite being in the country legally.
But when Ms Moreton's claim, which she earlier told the committee, was levelled at Ms Rudd by committee chair Yvette Cooper, she responded saying: "We don't have targets for removals". "I didn't see it as a systemic issue until very recently".