There have been many calls from Church leaders for the UK to open its doors to those who have had to flee violence.
In July, Islamic State (IS) issued a decree that all Christians in the area of its control must pay a special tax, convert to Islam or be killed.
Tens of thousands ended up fleeing, with many taking refuge in nearby Kurdish-controlled regions of Iraq.
The events led to the Bishop of Coventry, Rt Rev Christopher Cocksworth, asking a question in the House of Lords about what consideration the government is giving to resettling in the UK a proportion of those who have been displaced.
Lord Bates, who speaks in the House of Lords on behalf of the government, has responded this week.
He said: "There are no current plans to resettle those displaced from ISIS-controlled areas of Iraq.
"However, we are proud of the UK's record of offering protection to those genuinely in need, and the government will of course continue to consider asylum claims, including applications from Iraqi nationals suffering religious persecution, under our normal rules."
The idea of granting asylum was raised after France said it would take in refugees.
However, the offer wasn't supported by the Archbishop of Lyon, Cardinal Philippe Barbarin.
He said it could 'exacerbate the exodus' from Iraq, meaning that the country could be left with no Christians at all.