According to ESPN's Adam Schefter, Clowney can earn up to $15 million this season, which is well above what the Ravens and Saints could afford to spend. They have $866,586 and $642,307, respectively, in available salary cap space, per Spotrac.
Tom Pelissero and Ian Rapoport of NFL Network reported the Saints attempted to get creative:
"The sides discussed parameters of a deal in which Team X would've signed Clowney to a one-year, $15 million contract and paid him a $5 million signing bonus. Then, Team X would've immediately traded Clowney to the Saints, who would've sent Team X a second-round draft pick, as well as a player to take additional salary off New Orleans' books. The Saints would've paid Clowney's remaining $10 million salary."
Pelissero and Rapoport cited similar deals in which teams added a player largely to assume his salary figure and net a draft pick. However, those moves didn't involve a player signing with a franchise for the express purpose of going elsewhere.
"We felt like we got close," Saints head coach Sean Payton told reporters of New Orleans' pursuit of Clowney. "We weren't able to match the money, and that's one of the challenges every year. Mickey [Loomis] and Khai [Harley] did a great job working with [agent]."
Based on Florio's report, the Saints still would've missed out even if the NFL allowed the sign-and-trade to go through since he preferred Baltimore over New Orleans.