[Captain Ahab Jr]

They want to convert you to full time and not you asking

Just say you are really interested but they would need to make you an offer you can't refuse

Ball is in their court now, if you are as good as you say, they will know that and if they don't will soon realise it when they interview other people.

You have the advantage as you, your knowledge/experience and how you work is known to them which is worth a lot.