Given the amount of man-hours Arsène Wenger has always devoted to thinking about football, it is obvious he has spent some detailed time over the past few days mulling over quite what on earth to do with Mesut Özil.

The Arsenal manager has been in this predicament before – looking at a high-watermark transfer, a schemer of refinement and originality who arrived with the aura to suggest a team could be built around a special talent, who becomes increasingly difficult to accommodate.

Perhaps it would be useful to provide Özil with a video of Andrey Arshavin’s Arsenal career. What promise, what fanfare and, ultimately, what disillusionment. The Russian maverick found himself initially shunted out wide as he was not trusted to play in his favoured No10 position, then dropped to the bench and finally struggling even to make the squad. He ended up confessing that the whole experience had been “crushing”.

Record signings demand of a manager an extra responsibility to make the player work but there comes a time when his position needs careful – if uncomfortable – analysis about the extent to which he is helping the team. That time is now. The Özil-ometer plummeted during the past week on the back of two lackadaisical performances on the periphery against Manchester City and Borussia Dortmund. The perceived lack of effort, especially in moments when the team is collectively under pressure, is difficult to justify.

Wenger’s public position is to stoutly defend Özil. “Why should he be a scapegoat? For what?” he argues. “We’ve lost one game since 1 April. Let’s be realistic. We’ve come out of a very difficult preparation period with decisive games. What is difficult to manage today is that everybody knows absolutely everything and everybody judges people definitely on one game. You have to accept that football is played by human beings who have ups and downs like you have in your life.”

Now into his second season since that £42.5m record transfer from Real Madrid, there were two schools of thought about what to expect from this most nonchalant of luxury talents. Option one was that after a year of adaptation to the Premier League he would be ready to become the clever fulcrum of Arsenal’s gameplan. Option two was that he would suffer a World Cup hangover.

The reality certainly seems to be heavily weighted towards the latter – but Arsenal need to make sure that the situation is only temporary and not some deeper malaise that brings into question whether the marriage between club and player will ever be a truly happy one.

The Premier League has a history of flummoxed record signings. Özil is hardly the first example, with Fernando Torres’s ill-starred spell at Chelsea perhaps the most extreme of a number of expensive strikers that never fitted the bill at Stamford Bridge (Andriy Shevchenko and Hernán Crespo spring to mind).

Robinho’s time at Manchester City barely sparked. Juan Sebastián Verón at Manchester United was an experiment that was ended fairly quickly. The Andy Carroll venture at Liverpool seems to be a bad dream. These were all signings in the roughly £30m to £50m bracket that never worked. It happens.

So what is Wenger’s plan now? Does he keep Özil in the team and hope he summons some hunger, some rhythm? Or does he contemplate the double effect of dropping him? Not only would it give a player such as Alex Oxlade-Chamberlain or Tomas Rosicky the opportunity to add some drive to the collective, it would also be fascinating in the long run as a test of Özil’s character. Does he have the personality to react?

Even great players sometimes need to be challenged. An elite performer should feel affronted if he is taken out of the team. He should feel determined enough to prove doubters wrong and be fired up to demonstrate how talented he is. There is a famous story of when Dennis Bergkamp was in his early Arsenal years and Tony Adams told him in no uncertain terms that a player of his calibre ought to be winning things, not coasting along. Not long after that, Bergkamp was player of the year and had inspired Arsenal to win the Double.

That innate hunger to succeed is the big curiosity when it comes to Özil because even if he feels it, he doesn’t show it.

Wenger insists the current criticism is unjustified. “It’s a bit unfair because I believe that our offensive talents on Tuesday night [in Dortmund] were not in their best condition and they couldn’t express that talent. On the other hand it’s post-World Cup. He came back on 11 August. You know it takes a few months for them to get back to their best, that can happen. Many of the World Cup players don’t even play at the moment.”

The Arsenal manager urges the club’s fanbase to be forgiving. “They should not be concerned and just support him. I understand that you want your best players always to make the difference in every single game and we all go through periods where we are a bit less good. You help. A club is a union between players, supporters and directors. You have to be united and sometimes go through periods together where it goes a bit less well.”

Whether he plays, and how he plays, will be a significant plotline as Arsenal head to Villa Park this weekend.

While he prides himself on being a creator, the fact he has not yet scored in a Premier League away game and has no goal for Arsenal since last April is not easily acceptable for a £42.5m player who wants to be his team’s No10.

The man who covets the role of playmaker, whom Cristiano Ronaldo was so sorry to see leave the Bernabéu a year ago, needs to start making his own play happen for Arsenal.