If they haven't bothered to find a new place in the past 3-6 months that they knew they were moving then I wouldn't be surprised if they can't (read won't) find a new place and in 3-6 months they're still with you. Sorry.
They don't seem to care about how you feel about this so they're not going to be rushing to move out.
Think carefully about how much strain this might put on your relationship especially if it turns out to be a longer arrangement. Would it be better to cause some friction now and tell them they need to make alternative arrangements for accommodation? Or risk blowing up your relationship for good having them stay long term?