What!! Barcelona interested in Rodrygo? I haven't read this rumor but I'm sure it's just a rumor from some shady media outlet. The reason is Real Madrid might not agree to a loan deal and even if they do it's likely to be to another club. They only want to sell for their asking price, which is 100 million. With this in mind how can Barcelona spend that much money when their finances are so unstable? And I've heard that Barcelona main focus right now is Luis Diaz, who could have a lower release clause.
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.
If Rashford truly wants to join Barcelona and develop his career, I don't think a pay cut would be a problem for him. After all, Rashford would be delighted if Barcelona agreed to sign him, even if only on loan. Because, according to reports, Barcelona will offer Rashford a contract option for next season. Rashford would certainly be delighted to hear this.
I am not a head coach and don't have skills as well as vision of a head coach but in my opinion, I don't see any good contribution of Rashford for Barcelona. It's not like a necessary transfer that can help Barcelona improving their squad more. If it is done, it will cost Barcelona more money while with their exisiting financial crisis, they must self-limit money spent in order to boosting their financial crisis resolvement faster.