Nine of the 12 founding members, including all six Premier League clubs, withdrew from the proposed tournament after the plan sparked a furious backlash.
"I don't need to explain what a binding contract is, but effectively the clubs cannot leave," he told AS.
"Some of them, due to pressure, have said they're leaving. But this project, or one very similar, will move forward and I hope very soon."
The Real president has also claimed that it was 'not true' American investment bank JP Morgan had abandoned the competition aimed at rivalling the Champions League.
He said: "That's not true. There has been a time of reflection, like the twelve clubs. If something has to be changed, it will be done, but the Super League is the best project that we have thought that it can be done.
"What you have to do is recover the fans, the young people. And for that you have to change.
“If UEFA wants to do it with the project he said the other day, well, honestly, I neither understood it nor do I think it is a good solution. In addition, they want to start in 2024, and we will see what teams resist."