If there was a perfect time for Arsenal to get Rodrigo I would say it is now, since the arrival of Mbappe it was said that it will be Rodrigo who will be most likely sold off, last season his form and injury didn’t help him because he was injured all through out and didn’t get good minutes. Now that he is alive he is not looking like someone that Alonso values that much. The presence of even this young lad, Gonzalo is another big obstacle for him, so I think he will be open to leaving for game time.
Rodrygo is in an uncertain situation. First they said he was among Xabi Alonso's plans but now he doesn't look like that much.

He played for a really short amount of time in the Club World Cup until now.
Xabi Alonso cares about young players like him normally. But I don't know when he'll start giving him more chances. By the way how much money will Arsenal spend? They are already about to pay a lot of money for Gyökeres.