Realistically the club is going to have to make a final decision soon, whether their hand is forced by the EFL or not. ST's need be put out on sale soon as we're approaching peak signing season and without this revenue, the club is going to suffer in the long run. Like people say though the EFL will need to know where we're playing as the fixtures will obviously need to be altered depending on where we're playing as if we're at St. Andrew's we'll have to accommodate for clashing fixtures.
I suspect we'll hear something soon, whether it's this week or early next as for both reasons stated, this physically can't drag on any further.