Tbh, I think he'll sign a contract, possibly waiting 'til the autumn to see if he plays enough games/is worth a bit more wages, before doing so, but he might even sign next week if Pep persuades him.
But if it becomes apparent that he still isn't able to do what Pep wants, or his mother talks him out of staying, then a few months down the line should be enough time for he & Pep to agree it isn't working & start on an exit plan which works for both sides & we can work on replacing him.
All the top clubs will be trying to raise money, if they know he is available.