Talks with former Juventus and Tottenham chief Fabio Paratici appear to have collapsed.
Furlani said: “I said three days ago that we had not made any decisions on the director of sport, we are in a similar position to three days ago. We are focused on preparing for the season, choosing the right people in the right roles and someone who will be good for Milan.
“I can tell you the target is someone who can help us to win, so we are more focused on finding the right person than the timing of it.
“I repeat, the important thing is that it’s the right person. Clearly, we are in Italy and the Italian league, so that will be evaluated carefully.”
Furlani was also asked about coach Sergio Conceicao on Saturday before their draw at Fiorentina.
He replied: “Sergio is our coach, we are focused on doing well until the end of the season. Until proven otherwise, he is our coach."