After Al Nassr committed €500 million to Ronaldo, he also made it a condition that the club bring in strong signings. It seems Ronaldo is now trying to bring Rodrygo to Al Nassr. Hopefully they sign him, because I think if Rodrygo joins Arsenal, he may disrupt the team chemistry. Apparently, Real Madrid is asking €90 million for him. Arsenal shouldn't be paying that kind of money anyway. One thing is clear, Rodrygo's Real Madrid career is over. He will definitely be transferring to another club in this window.
Perhaps Rodrygo doesn't fit in Xabi Alonso's pattern and this is common to happen to player(s) when a new coach comes into a club. Rodrygo just 24 is to me too young to take his career to the Saudi Pro league, and I agree, Arsenal won't be a favourable place for him even if Arsenal can afford his fees. Where I will love to see him play is PSG or Bayern Munich.
Many Real Madrid fans are reluctant to see Rodrygo leave Real Madrid, as he's the player Real Madrid needs when they're struggling. He's often the solution; he's arguably one of Real Madrid's impressive supersubs.
However, as you said, he's still a young player with a long career ahead of him, so leaving Real Madrid is the best option for him to break into the first team. Even if he were to leave Real Madrid, it's unlikely he'd go to Saudi Arabia, as he still wants to pursue a career in Europe. I think Arsenal, PSG, and Bayern Munich are the best options for Rodrygo right now, as he's a player with potential, but unfortunately, he's been overshadowed by Mbappé and Vini at Real Madrid.