No to Arsenal rejects.
I would just try to shed off more salaries this month (negotiate contracts with Busi&Co, loan Pjanic, try to loan Cou and Umtiti) and stay with what we have for the season. Don't think anyone we can get now would clearly improve the team and wouldn't just sign for the sake of signing. Rather wait and see if our situation will improve enough and maybe in January we can sign someone on expiring contract. Either on a free contract for next season or pay a small fee to get him immediately. Don't see likes of Mbappe, Goretzka and Camavinga available but obviously if we could freely negotiate witih one or more of them from January would be stupid at least not to try even if our chances for landing them wouldn't be exactly high. It's more likely we could get someone like Boubacar Kamara, Khephren Thuram or Ihattaren though.
Use similar philosophy in 2022 and target players with a year or two left on their contracts. Stay in touch with players's agents and see what they would want and if they are willing to sign for us. We should also look for players who are Barca fans like Pedri and Demir and would come here even if they could earn more in other clubs. Our recruitment should be based on the players who want to play for Barca not motivated mostly by money. Promise them (especially if they're still younger and not totally proven) a fair chance to compete for first team minutes they probably won't get in other currently more stacked teams. While nobody will have a pulling power of Messi I think players like FDJ, Pedri and Ansu (if he fully recovers) are still a very good selling point for the club in recruitment of the players. And then having a chance to replace Pique, Alba or Busi in the lineup longterm as well.
And further, look for players at smaller, known selling clubs like Salzburg who OTOH are still setting pretty "normal" prices in this crazy market. Daka (30m) is their record transfer. If we can get Adeyemi for close to that fee we should be all over him if we can afford him next year. Mohamed Camara is also interesting to me and there are obvious other players worth following as well.
Only player I'd be willing to go into a bidding war for with other clubs is Haaland. And I could fully see him also being somewhere in the back of Laporta's minds when he made a decision to let Messi go. From a sporting POV would clearly be easier to get Haaland with Messi still around but from financial standpoint this just wouldn't be possible. I still don't see us having big chances to get him but with some other moves on the market (Lukaku to Chelsea, Kane possibly to City and Mbappe possibly to RM) at least on paper there should be less competition for him.
If we won't get him it won't be the end of the world though. There are some younger strikers still in smaller clubs who we could target. I've not seen much of him but from what I did the one I really like is Adam Hlozek. He could become special but tbh I think an EPL club will sooner or later offer more than what we could afford/would be willing to pay for still a pretty unproven player on a top level.