He has been likened to a tortoise, a hare, an owl, a clownfish and a chameleon, and it all started in a monkey's cage. It could be one of Aesop's fables. Instead, it is Ozil's. The story of the Turk who represents a new Germany and a new Real Madrid, yet also represents something older, something disappearing. Mesut Ozil: future and past in one, a street footballer whose director general, Jorge Valdano, believes "will define the next decade" and whose team-mate Xabi Alonso describes as "the kind of player you don't find these days". The playmaker who joined Madrid for €15m.

That figure, about £13.2m, was a bargain, possibly last summer's best business. To put that into context: it is less than a third of what Chelsea paid for Fernando Torres, less than half the amount Aston Villa paid for James Milner, less than a quarter of the €65m Kaká cost Madrid the previous summer – and no one would swap now. All for one of the World Cup's finest performers; who, eight months on, stakes a claim to be La Liga's outstanding player. Certainly beyond Cristiano Ronaldo and Lionel Messi. He is so good they are likening him to Zinedine Zidane.

Speaking in German – his Spanish still limited to a pre-prepared stuttering, if crowd-pleasing, "I want to win titles with Real Madrid" – Ozil says: "I'm not Zidane yet." He could hardly say otherwise. In Madrid, the comparison is powerful and Ozil is still in his first year at a new club and in a new country. "Zidane was world-class," he says, "I haven't done anything yet. I'm here to develop, I still have so much to prove."

Except that is partly the point. Even when Ozil's talent has been seen only in flashes, they have been flashes that win over a Spanish crowd – more enamoured with artistry than elsewhere. "He's the kind of player who goes down well," Valdano says, "even opponents like watching him." Besides, he has done more than most anticipated. It is the relative consistency that has surprised, the speed of adaptation. Hardly surprising that a partisan press is now getting so excited.

A couple of weeks ago, Marca splashed its cover with cartoons of every Madrid player, alongside their supposed nicknames. In the middle was Ozil – footballer turned fish, orange stripes and goggle-eyes. The headline said it all: Real Madrid were "Nemo's Gang". The following day, he was portrayed gazing at the Balon d'Or, the trophy that "awaits him".

It was a significant break from the editorial line: someone other than Ronaldo centre stage, the leader. It was also an exaggeration, but there was something in it – and not just because Ronaldo was missing when Ozil, all graceful movement and clever passing, masterminded the destruction of Racing Santander, 3-1, in La Liga last month.

"Ozil," says Alvaro Arbeloa, "is a scandalously good player. I wouldn't say the media jumped on board too quickly. In fact, you've taken your time to realise just how good he is. Then again, we see him in training every day, you only see him once a week. We knew he was special straight away. Sometimes it can seem like Ronaldo is the only player here, but there are other good players too – and Ozil is bueno, bueno."

Ozil always has been. The man a computer game called the owl, a commentator claimed had chameleon eyes – bulging but all-seeing – and a German philosopher described as owning a turtle's face, began playing in Gelsenkirchen in the Ruhr valley, where he was born in 1988, the son of Turkish immigrants. The mines have closed down now, but the tower still looms over Bismark; a largely Turkish neighbourhood, with a small, rough gravel football pitch enclosed by hostile wire fences, where the ball never went out and games never ended. A pitch they called the Affenkäfig: the monkey cage.

Ralf Maraun, one of Ozil's first youth coaches, says he is the "classic street player – timid and small, but incredibly talented". If he was Argentinian you'd call him potrero, learning close control and cunning as a necessity. Anything but regimented, except that he was regimented, too: he joined DJK Westphalia 04 at seven. As Ozil has put it: "My technique and feel for the ball is the Turkish side of my game; the discipline and attitude all come from Germany." And when it came to the contested decision over international football, Ozil responded: "I was made as a footballer here."

Germany was fine: Ozil was the Bundesliga's outstanding performer last year, providing 17 assists. Spain was a step again. For a start, he spoke no Spanish. On the opening day, he was left out of the Real Madrid side, José Mourinho admitting he could not converse with the playmaker. Between them, his staff spoke a handful of languages, but German was not one of them. Meanwhile, Ozil's English is limited; even his German is not perfect – his career began with his father shouting instructions in Turkish.

Language was not the only problem. Perhaps there should have been more faith: why should he not adapt to Spain as his family adapted to Germany?

It is not as if he had made it this far without resolve. But Ozil, far from outgoing – a man who says his favourite film is The Karate Kid and is a quiet, practising Muslim – was dismissed. Even those enamoured by his football in Germany thought he would struggle. He is only a kid – he turns 23 next season – and the pressure would be huge. The journey from the monkey cage to the bear pit was a long one.

They were not alone. The Spanish league's style suits him, but success was not guaranteed. Certainly not success like this. Real Madrid signed Ozil, impressed by the World Cup and attracted by the price tag – another in a long line of media-puntas, another must-have accessory. Although his age was further attraction, the truth is, they did not necessarily expect to talk about him as the artificer of the future. Now, they do.

The main reason Ozil was cheap and available was his refusal to renew his contract with Werder Bremen – but it was also because of concerns. Pay €15m for Ozil? It looks so obvious now; it was less obvious then. Arsenal watched him and liked him; Barcelona, too. Barça were his club, Messi his hero, but doubts lingered and priorities lay elsewhere. In Madrid, they were quick and Mourinho encouraged the pursuit. They took advantage of the question marks that remained about a player whose brilliance was often seen in passing.

There is certainly brilliance in his passing. Madrid are a side built to counterattack and who, as the season has progressed, have found doing so harder. Teams are waiting for them now, sitting deep and closing up. That has required a different skill – Ozil's skill. In a team of athletes, it is Ozil, alongside Alonso, who is the aesthete, providing the subtlety and the vision, giving flow to the physicality, looking for the angled pass, slipped silently beyond a sea of legs. Coming in from either side, moving freely, the kind of footballer who does not just play well, but makes others play better, too.

"He understands the game, sees things, combines and thrives between the lines, unlocking teams," Alonso says. Valdano highlights his "collective play", the ability to "create football". "Ozil," Mourinho says, "is unique. There is no copy of him – not even a bad copy."

That is why the Portuguese coach has protected and nurtured him carefully, even as he has used him. Ronaldo's injury means Ozil is now the only Real Madrid player to have appeared in every league game this season, yet he has lasted 90 minutes only five times. It has brought about a perceptible shift in style – bringing Ozil to the fore. With every match, he appears to take on greater significance. Under Mourinho, his confidence has grown. Although still slight, so have his muscles.

"Ozil has evolved," Mourinho continues. "Before, there were details, glimpses of his class, but he mixed those with quieter moments. Now he stands out for his dynamism and the continuity in his game." The cumulative effect of his contributions, not always consistent, allowed him to emerge – if not in performances, certainly into the collective consciousness. It is not just about playing well, it is about people noticing.

A relatively discreet if steady start had the happy consequence of releasing him from the need to live up to his own early hype. Sometimes a debut hat-trick is the worse thing that can happen here. Now what appeared slow looks quick. It has still been only eight months, after all.

Silently, almost by stealth, his statistics started to stand out. Now they are inescapable: nine goals in all competitions and 11 league assists, plus three in Europe and one in the Spanish Cup, speak greater volumes than he does. Only Messi has provided more assists in La Liga.

Quick-footed, blessed with a soft touch, Ozil moves with speed and smoothness, two-footed and agile. He has been involved in 25 of Madrid's 101 goals. In total, he has created 100 goalscoring opportunities, more than anyone else in Spain. "Ozil is playing absolutely fantastic football," Mourinho says. "Real Madrid have a great player – and for a long, long time."