The Catalan giants apparently had an agreement in place with Juventus since the 2014/15 season, giving them priority when it came to buying the player.
Pogba recently became the world's most expensive footballer when he rejoined Manchester United from The Old Lady for a fee of £89million.
"Last year we reached an agreement with Juventus: if they wanted to sell Pogba we would have a priority," Soler said.
"That was the commitment that we had. Juve did not want to sell the player and we didn't have the need to sign him.
"Barcelona has always had a great relationship with Juventus. If we would have wanted to do the deal, nobody could advance us.
"We signed six players with €120million. If one club can pay €120m for one player [it] will be very difficult to sign great players."