Real are in a "new golden age" according to club president Florentino Perez, who added their "legacy has flourished" in recent years.
The Spanish giants are regularly a dominant force both domestically and in Europe and, in the past decade, have won the Champions League six times and La Liga four.
They have also often had some of the world's best players for them and this summer brought in France star Mbappe, who had scored 256 goals in 308 games at PSG before leaving the French side earlier this year.
"We are experiencing a new golden age having won 56 trophies in the last 14 seasons: 29 trophies in football and 27 in basketball," Perez said at Real Madrid's general assembly on Sunday.
"The legacy of Real Madrid has flourished in recent years."
Despite their recent success, Real have not had the best of starts to the current season.
They won both La Liga and the Champions League last season but are currently second to Barcelona in the former and 18th in the league phase of the latter.
The format of the Champions League was changed for this season, and Perez believes the competition has been damaged as a result.
"The new Champions League format has shown, as we predicted, that it is not the solution to the problems," he added.
"Uefa has increased the number of matches, but each match counts for much less than before. And the competition will only stir fans' passion at the end of the season and not at the beginning, as one would expect."
Perez has long been committed to a European Super League (ESL) and Real were one of 12 European clubs to sign up to the ESL in April 2021 but it collapsed after a fan backlash.
Last year, the European Court of Justice ruled that Uefa and Fifa banning clubs from joining the ESL was unlawful.
On Sunday, Perez reiterated his belief in the competition, saying: "We have a unique opportunity to develop a new model of governance and competition that prioritises both the wellbeing of the players and the passion and excitement of the fans.
"There is a real opportunity to change course, to revitalise football and restore it to grandeur. And the sooner we do it, the better.”