Montolivo has pulled back from contract talks in the last week.
"We hope it can soon all fall into place," Corvino told Viola Gol.
"We already worked so hard on these negotiations, but now we are perplexed. Montolivo and his agent asked for more time to think and we accept that."
It is reported that Montolivo was prompted to reconsider by interest from Inter and Juventus.
"This situation just cannot exist," insisted the director of sport.
"I am optimistic based on the professional behaviour of Montolivo and his agent, Giovanni Branchini."