I received a formal offer for my PA position a week after I interviewed for it (it was the minimum time they had to leave the position open for others to apply for even though they already knew they wanted me), but I didn't actually start training as a PA until a month later because my FA TL couldn't spare me until then.
Not positive what the hold up would be in your case, unless they've decided to keep interviewing or maybe they are going to drop the spot all together? Dunno. With a PA, it seems you would want to fill that ASAP because there's so much extra tasks a PA has to do as opposed to a regular Market TM; but maybe it's not that way in your store.
With me, once I talked to my TL & the CTL about my interest in the open PA position, I think I had the interviews a few days later & was offered the position about 10 minutes after my 2nd interview and started the training the next week. My CTL is also one of the favorites among the ETL's and is able to move things along that he wants to happen.