Rodrygo is talented and professional, and can be a transfer target of many big clubs. I am not surprising if Barcelona want to have Rodrygo and in history there were transfers between Barcelona and Real Madrid so there is chance for such a transfer of Rodrgyo from Real Madrid to Barcelona this summer.
The main barrier is transfer price that is very expensive and if Barcelona did not buy Nico Williams by having limited budget, I don't think they will be ready to purchase Rodrygo with a big money to spend. It's unrealistic and logic interference makes me thinking more about rumors. Rodrgyo has high possibility of moving out of Real Madrid but his destination will not be Barcelona.
I do not see this possibility. Since it is now almost certain that Rashford is coming to Barcelona on loan, so there is absolutely no chance for Barcelona to buy Rodrygo now. After having talented attackers like Torres, Lewandowski, Yamal, Raphinha and Rashford, does Barcelona need Rodrygo? Lewa, Raphinha and Yamal will be in the starting XI for sure. We still do not know how Hansi Flick will use Rashford. In such a situation, why would Barcelona waste money by buying Rodrygo and keeping him on the bench? Also, Barcelona's financial situation is not good at all. Where will Barcelona get the money to buy Rodrygo at such a huge amount? So I consider this just a rumor.
I also believe the speculation about Rodrygo transfer to Barcelona is just a rumor. Even if Barcelona had enough funds to make the transfer happen, they couldn't do it because they're blocked by spending restrictions. Besides, Barcelona would also have to sell two or three other players first to balance their salary structure. Rodrygo is just not a realistic target for them right now. Currently, Barcelona is probably trying to register Rashford with La Liga first, and Hansi Flick doesn't seem to be looking for any other additions to his attack.