Neymar is an "opportunity" in this transfer market for both Barça and Real Madrid. But whilst the Camp Nou side's squad is complete (aside from a couple of outgoings), at the Santiago Bernabeu they still haven't brought in that megastar to replace Cristiano Ronaldo (12 months too late). That's why Madrid need Neymar more than Barça do. Florentino Perez, in particular, knows he got it wrong when he didn't sign a new star. Hazard is a very good player, Jovic has to the potential to be world-class, but neither one of them could lead Zidane's new project.
Following Manchester United's 'no' to a deal for Paul Pogba, Florentino has been forced to find a new explosive signing. That's why Neymar is an excellent option. Not just on a footballing level but also the brand and star power he brings. Signing Neymar would represent a double victory for Florentino: presenting his new leader to the fans after a poor preseason but also the chance to say they beat Barça to Neymar.
Barça don't 'need' Neymar. It's clear that he would be a great signing and would generate a lot of excitement for Barça fans, but Valverde's third season doesn't include Neymar. Griezmann and De Jong were the two signings that Valverde felt he needed. If Neymar comes, even better, but if he doesn't, it isn't a big loss either. It might cause a bid of damage to morale if he ends up at Madrid though. That's why Bartomeu will fight until the last second as long the Brazilian doesn't sign off on the millions Florentino Perez is currently offering.