The Italy international was linked with the two-time Premier League champions during the most recent transfer window, while Chelsea are rumoured to be considering a big-money bid for the defender in January.
Soriano has now claimed that Bonucci tried to instigate a switch to the Etihad Stadium due to his desire to play under manager Pep Guardiola, but Juventus managed to keep hold of their man.
"At the moment there are a lot of players that want to play under Pep," Soriano told RAC1. "The Italian central defender Bonucci wants to play for him and he called us.
"I called the Juventus sporting director [Fabio Paratici] and he told me they didn't want to sell. There ended the story."
Bonucci is believed to have begun talks with Juve regarding a new contract.