Nuno has been outspoken over Forest's slow summer market campaign.
It's been suggested Marinakis is unhappy with Nuno airing his complaints in public, leading to speculation about the manager's future.
But when asked if Nuno can take the club forward, Marinakis told TNT: "Yes, he has been successful and we have done things we have enjoyed. Now we can afford to do things that we enjoy.
"Everything is solid. We all want Nottingham to succeed. We are here in the good days but we are even closer in the difficult days, so personally I don't see a problem.
"We are all together, united, and we'll make some corrective actions and everything will be smooth and ready to go.
"We have a solid relationship. Of course, sometimes we can be nervous, say one thing, say another, but what counts at the end of the day is the real relationship between me and Nuno, between Nuno and the players and between the players and ourselves."