Chelsea goalkeeper Petrovic has ended up with Bournemouth. I assume they are planning to make him their main GK. Because they are going to pay 25 million pounds.
I think he is a really good choice for them and he would also be happy to play Premier League football regularly.

He was the highest rated GK of the season in the Ligue 1 last season.
I read a rumor that Arsenal have agreed with Viktor Gyokeres. Maybe his position is different from Rodrygo, but Gyokeres has been priced at 60 million euros. So if they buy Rodrygo again it seems that they are spending too much money. I'm not sure they will sign Rodrygo at that price. They have signed Kepa, Zubimendi and most recently Gyokeres. I don't see Arsenal having a big budget every season.
Besides Arsenal is still haggling with Sporting to pay as low fee as possible. I don't know how much their budget is but FFP would be their main concern to be able to register all their new signings.
I'm not sure whether they really need Rodrygo currently. They have Saka on the right wing. Let's say Martinelli left then I would find it more logical for that space.