Claudio Ranieri will step aside at the end of the season to take up a front office post.
Asked for an update on their coaching search, Ghisolfi said ahead of last night's win against Fiorentina: "I'm not here to confirm or deny any names, all I can say to our fans is that this is an important decision.
"We are working on it. We want to build something, an organization with humility and passion.
"We have clear ideas, the coach and the club owners are 100 percent in agreement. Everything will be announced at the right time."
Confidence around Svilar
When asked if it is a name that has been mentioned in the media, Ghisolfi also told Sky Italia: "As I said, I don't want to mention names. We are working on the future, but now we have to focus on the present, because this is a lively and exciting match (against Fiorentina tonight)."
Ghisolfi also provided an update on negotiations with goalkeeper Mile Svilar over a new deal.
He added, "We are in no hurry because the contract runs until 2027. We are talking, he wants to stay at Roma and we want to build the future with him.
"He deserves a new contract at the same time as we want to build with financial stability, so we are negotiating."