The former Liverpool boss is a candidate to succeed Beppe Iachini.
"Benitez is one possibility," Garrone told reporters on Tuesday at Genoa's Science Expo.
"There is nothing concrete, but there has been contact, it is in progress. It does not mean that tomorrow we will see him here, there are no trips planned. But, we care about the team.
"[His arrival] remains to be seen, though. I cannot deny that we are interested, but there's still a little way to go and I cannot say that it will necessarily end in a positive way."