The Bianconeri have been linked with Alonso all summer and held talks with the Spaniard over a possible move to Turin.
However, the deal stalled after they failed to agree a fee with Liverpool and Juventus ended up switching targets by signing Christian Poulsen.
"Everyone knows that the transfer market ends on August 31," said Cobolli Gigli.
"But if I have to be honest, unless something extraordinary happens, we can say that we have concluded our transfer activity."