Pompey have been searching for a buyer since November when previous owner Vladimir Antonov stepped down after the club's parent company Convers Sport Initiatives entered administration.
Andonikou told Sky Sports News: "We're not that far away so if you could all bare with us for another day or so I'm sure we can reveal their identity and their ambitions in terms of purchasing the club.
"We've been talking to this party for a number of weeks now. We want to bring financial stability to the club. They've satisfied us in terms of their financial potential and we've now got to negotiate a deal."
Andonikou dismissed speculation the prospective owners have a Russian connection and hinted they have not shown any interest in buying a football club before.
He added: "The Football League are going to have to ratify the purchases in terms of the fit and proper persons test so there will be a number of layers for the party to pass before they can actually purchase the club."