The Catalan giants activated the France international's €120m (£103m) release clause in 2019, but he has largely struggled to make his mark at Camp Nou and returned to Atletico on loan over the summer.
Reverter has claimed that Barcelona, under the previous board, could not afford to sign Griezmann and had to "go looking for a loan" in order to complete the deal.
"We have the feeling that when they (the previous board) were signing players, they did not know if they could afford to sign them," Reverter told reporters.
"That was the case for Griezmann, who on the night they signed him they realised that there was no money to pay for the transfer. They had to go looking for a loan of €85m (£72m) to cover that signing."
Griezmann still has three years left to run on his contract at Barcelona, but Atletico have the option to re-sign the World Cup winner on a permanent basis next summer. body check tags ::