Madrid manager Jose Mourinho has been unable to wrestle the La Liga and Champions League crown from Barcelona and opposite number Pep Guardiola in recent seasons.
However, former Croatian and Madrid goal poacher Suker believes that Real now possess the greater desire and ambition to fight for the biggest silverware in football.
"Madrid are very strong at the moment," he told Marca in an interview.
"They have gone on a great run of results and that's not by chance; they are first in La Liga and in their Champions League group, playing very good football and scoring lots of goals. Real Madrid have more hunger than Barcelona now."
"Mourinho is a winner," he said. "He has come to Spain to win La Liga - and he'll achieve it.
"He is the ideal coach for this team and [Madrid president] Florentino Perez hasn't made a mistake - he signed the best. Mourinho's work is still in progress, but I see them winning either the league or the Champions League, and I think they will win La Liga because they are more consistent [than Barca]."
The former Arsenal frontman is confident that the nine-time European champions can usurp the Catalan giants when the two sides face off in the El Clasico at the Santiago Bernabeu on December 10.
"It's simple," he said. "You have to take the ball off them and score goals. The team that has possession is the team with the best chance of winning. And Madrid can do that."
Suker is no stranger to the Madrid fabric, having plundered in 49 goals in 106 appearances for the Spanish side between 1996 and 1999.
He helped the club to their seventh Champions League crown in 1998 and also claimed one La Liga title, one Spanish Supercopa and an Intercontinental Cup crown.