Ecclestone, 87, was ousted as the sport's long time 'supremo' following the arrival of new owners Liberty Media.
Now with Marchionne at loggerheads with Liberty and Ferrari threatening to quit, Ecclestone met with the Italian-Canadian at the recent Geneva motor show.
La Gazzetta dello Sport quotes Ecclestone as saying: "It's easy to imagine the things we spoke about because, as ever with Sergio, there was a total convergence."
Marchionne told the press he had met with a "very fit Ecclestone".
When asked about Liberty's plans for the future of F1, Ecclestone said: "I too dream of a world championship with 20 teams and 20 different engines. But that's utopia.
"Perhaps Liberty Media are thinking of doing things that I cannot imagine."
Ecclestone said that Liberty should not try to find out if Marchionne's quit threat is real.
"Marchionne is someone who, when he says something, he does it and does not look back. Liberty should therefore be careful about what they do," he said.
"I've been close to Ferrari since the days of Enzo. F1 - or my F1 - was a company that distributed large dividends to its shareholders. Of course, there were always quarrels and discussions, but in the end we always came out best.
"Marchionne knows my position. Sergio knows what whatever he wants to do I will be there. We have discussed many things."
When asked about Liberty's flagging financial accounts, Ecclestone said: "Many of the existing contracts were made by me and passed to them. At that time, the money was there."
Much of that money was given to Ferrari as bonuses, which Liberty would now like to take away.
"It's not a bonus," Ecclestone insisted. "It was a prize for participation - because Ferrari has always been there.
"I never gave anything away - when I gave something there was always a reason."
He would not say much that was flattering about Liberty, including the decision to ban 'grid girls'.
"I no longer have direct involvement so I just see what others see. Things that seem incomprehensible. The grid girls [ban] did not seem like a brilliant idea."
Asked if there is anything positive, Ecclestone answered: "I have not seen much.
"I see that they are throwing a lot of money away. My FOM was always less than 30 people. A small but efficient structure."
Liberty, on the other hand, has a staff of 150 and growing.
"They're probably not necessary," said Ecclestone. "Unless they can produce 3-4 times what I produced in a short amount of time."
The 2018 season begins this weekend in Melbourne.