A potential transfer to Los Blancos made it to the final stages before ultimately being aborted by Madrid, according to Perez.
"Neymar passed a medical with Madrid. We tried for him to come, but we saw at one point that it was not possible and we withdrew (from the deal)," Perez told Onda Cero.
Neymar ultimately joined Barca in the summer of 2013, with Madrid electing to make a big-money splash later on in that same transfer window.
Unable to sign the Brazilian, Perez sanctioned a then-world record transfer for then-Tottenham man Gareth Bale in September 2013. The Welsh attacker's move to Madrid late in the transfer window followed high-profile moves of Sergio Ramos (2005) and Luka Modric (2012) that came in just under the wire at the end of the summer.
It's why Perez isn't too worried about the lack of movement at Santiago Bernabeu so far during this transfer window.
“I like the market all the way until August 31. There’s a long way to go,” he said.
As for Bale, Perez said that he wasn't disappointed with the 27-year-old's lack of production in an injury-ravaged campaign.
Overall, Perez said, the club's brass are happy with their investment in the Welsh attacker.
“Bale’s tendons went," he said. "He had bad luck this season, but he has given us much satisfaction.”