Arsenal are indeed the closest, and rumor has it they have made an offer to Madrid. But not only Arsenal, Liverpool was also rumored to be interested, but they are also waiting for the completion of the transfer of their released players. Not only from the Premier League, Barcelona is also rumored to be interested in bringing Rodrygo, although I am also not quite sure of their seriousness.
Many European clubs still have an interest in Rodrygo. I think there is no reason for him to move to Saudi to enrich himself at an age that is still very productive for competition in Europe's top leagues.
A sports news outlet football.london claimed that Barcelona is also interested in signing the Brazilian international. Rodrygo said he respects Real Madrid and wants to remain in the club. But it seems Xabi Alonso prefers other strikers, as shown in the FIFA World Club event. So he might want to leave for a place where he would be appreciated more. Real might be open to let him leave for €100m (£85m), and it might be hard for clubs to afford that amount, except there are other agreements, like player swaps.Many European clubs still have an interest in Rodrygo. I think there is no reason for him to move to Saudi to enrich himself at an age that is still very productive for competition in Europe's top leagues.
Several Premier League teams are currently interested in Rodrygo, but so far there haven't been any strong rumors in the media. However, I'm sure whatever happens, there's a strong possibility that Rodrygo will leave for a new team next season. There could be a surprise at the end of the transfer window.