It is La Décima season in the Spanish capital. Around this time of year, ritual has it that there is much discussion of "the 10th". Yearnings are expressed. Knowing looks are exchanged. Details are analysed. More or less anyone with even the vaguest affiliation for Real Madrid knows exactly what is being referenced by the word décima – "10th". There is no need for any elaboration whatsoever.

When Real Madrid won their ninth European title courtesy of the most breathtaking swish of Zinedine Zidane's left foot just over a decade ago, nobody would have imagined that it would take so long to reach double figures. At the time the original galáctico project was in full swing, with Zidane, Luis Figo and Roberto Carlos illuminating the scene, and each summer the world would wait to see which shimmering superstar Real would pounce for next. And as for their friends from Catalonia, the scoreline in terms of European Cups at that point was Real Madrid 9 Barcelona 1. In 2002 there was no reason to predict that the most decorated club in Europe would fall away over the next few years.

It seems strange to recall that Real Madrid endured a prolonged period of soul searching in this competition between 2005 and 2010 (a phase worsened by Barcelona starting their current collection of trophies). For five years in a row they were bamboozled at the last 16 stage. Some of those exits were deeply embarrassing as they capitulated against Arsenal, Roma and Lyon when they were clear favourites.

Enter José Mourinho. Fresh from a brilliantly devised Champions League triumph with Internazionale delivered, of all places, at the Bernabéu. It was in that press room after the celebrations, still wearing his Inter tie and blazer, that he announced: "I want to become the only coach to win the Champions League with three different clubs." Every fan and his dog knew which club was supposed to provide him with his hat-trick.

Although Mourinho is credited with rebooting Real sufficiently to reclaim La Liga from Barcelona, arguably his progress line in Europe is more impressive than domestically. In the past two seasons, Real have regained European credibility by at least getting significantly closer to the prize. Semi-final heartache – inflicted as it was, first, by Barcelona and then a tormenting penalty shootout against Bayern Munich – is not something they wish to mull over. But overall, Real under Mourinho have shown they mean business again on the European stage.

At times during the last campaign they were lethal on the counterattack, with Xabi Alonso's range of passing the perfect platform from which Cristiano Ronaldo could strut his stuff, Mesut Ozil could pull strings and Karim Benzema could burst away. As Manchester City, their opponents on Tuesday in the first round of this classic group will be aware, they scored 24 goals from their six home matches last season. Now that they have unclasped the Barcelona monkey from their back by finishing above their grand foes to clinch La Liga, and with a settled team guided by a coach who is as obsessed by the Champions League as they are, this appears to be as good a time as any for Real to believe the 10th really might happen.

The experience of winning, and another season of bonding the team's way of playing, can only be an advantage. But by their expectations, they have not enjoyed a smooth start to the campaign. They lost 1-0 at Sevilla on Saturday and are eight points behind Barcelona. Being held to a draw by Valencia, and defeated at Getafe had already whacked up the pressure.

Then came the Ronaldo melodrama. This time last year, as Real embarked on their latest quest, one of the headlines in AS was "Cristiano smells La Décima". There has been a rather less uplifting whiff around Cristiano lately, as revelations about his unhappiness have dominated the Bernabéu landscape.

Naturally, his team-mates were moved to dampen down the impact. "You have to keep things in perspective," offered Alonso. "There's too much exaggeration. He's the same player as 10 days ago or two months. What we experience as a team is very different to the image sold outside. He seems totally normal to me."

Ronaldo is set for new contract talks, and nobody expects much of a backlash when he makes his first appearance in front of the home fans for the game against City. "I have no doubt that the public's reaction will be fantastic," Alonso said diplomatically.

The other issue of concern is Ozil's fatigue. The German has been below par but Mourinho now has an option in new arrival Luka Modric. The coach was mischievous when he was asked precisely where the Croatian will fit into the team. "He will play in a position that is his," Mourinho quipped. "I'm sure he won't be at left-back or centre-forward." He certainly has the poise to influence games at the highest level.

One of the criticisms levelled (somewhat harshly) at Real during last season's Champions League campaign was that when it came to the crunch, in the semi-final against Bayern, they lost their nerve. Experienced men such as Ronaldo, Kaká and Sergio Ramos missed penalties.

The current Real squad have six Champions League winners in their ranks. Notably, though, only Iker Casillas, who came on as a substitute in the 2002 final, won his title in the Madrid white. Ronaldo was with Manchester United, Kaká with Milan, Alonso with Liverpool, Ricardo Carvalho with Porto, and Michael Essien as an unused substitute with Chelsea.

Real recently announced they posted a record revenue of more than ¤500m (£405m) during last season. They claimed to generate "the biggest sum of any sporting institution in the world". There is no doubt these figures are impressive but, in the end, the only number that really drives them is shorter and to the point: 10.