Forest haven't competed in Europe since the days of the great Brian Clough.
But Marinakis, whose Greek club Olympiacos won the Europa Conference League last season, told BBC Sport: "Why not? We did it with Olympiacos, and that was the first time ever a Greek team had won a European cup. We were the underdogs; nobody believed it.
“All these years when I was saying that we (Olympiacos) would eventually win a European title, a lot of people were laughing. That’s better because it means less competition. It is better to be underestimated. We did it.
“Why not? Nottingham Forest have a very good team. If we perform well in the Premier League and we get into a European competition, then why not?
“We have what is needed to go all the way. I really believe that. But the first target is to perform well in the Premier League, and then if Europe comes we will look forward to performing (in it).”