Watching Arsenal coast to victory at Tottenham on Saturday, you could have been forgiven for forgetting that they are without a permanent manager. That is testament to the job Renée Slegers has done in interim charge, in overseeing five wins from six games without defeat, and inevitably speculation about her future will heighten.

Whether it is the jubilant Arsenal fans packed on to the London overground saying it was “her job to lose”, commenters on the Guardian’s match report echoing similar views, or people airing their thoughts on social media, it is clear there is a growing tide of fans, pundits and neutral observers calling for the Dutchwoman to be given the permanent job.

Arsenal, though, would be wise not to rush into appointing the 35-year-old, despite the hugely impressive way in which she has conducted herself. Slegers has been virtually flawless since stepping up but the club should be careful not to overreact to such a strong month, because rewarding her with, say, a three-year contract could prove to be a mistake in long term, for no reason other than that Arsenal should not settle for anything less than the best person for the job in the world. Only that should suffice for a club whose ambition should be to win the Champions League within the next two to three years, not merely the November manager of the month award.

There is a strong case that the Arsenal job is the biggest in women’s club football right now, given that they are attracting the largest average attendances of any team on the planet, are the most successful club in England in terms of trophies and have been underachieving relatively in recent years.

There is a long list of things Slegers has brought that deserve huge credit, from the composed, calm and professional manner with which she has handled media duties, to clever tactical tweaks such as deploying Steph Catley as the left-sided centre-half rather than at left-back, and the confidence she appears to have given the players. She has also been unafraid to make bold selection decisions, such as omitting Beth Mead from the XI at Spurs or withdrawing the captain Kim Little at half-time there to ensure Kyra Cooney-Cross could play a significant portion of minutes from the bench.

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Above all, she has brought back that winning feeling to a team who are playing to their strengths, keeping things relatively simple, and has put smiles back on faces for a side who – for whatever reasons – did not look happy a month ago. The players have spoken highly of her, and she clearly has their trust, which is half the battle for any coach.

Having said all that, being an interim head coach is different from having the permanent role. If Arsenal decide after exhausting every immediate possibility that Slegers is the best candidate, it still feels too soon to offer a long-term deal. Until the end of the season, perhaps, would be an adequate period to assess how Slegers copes with setbacks and challenges.

Slegers has been repeatedly questioned about the vacancy and has reiterated that her focus is on the games up to the international break. Asked on Saturday whether anything had changed regarding her future, she said: “No. The block [of games] has gone really well so far. And now we have one game ahead of us, and we’re going to do everything to get a good performance and good result again.”

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Everything we hear about Arsenal’s search to replace Jonas Eidevall is that it will be extensive, patient and global. Multiple sources have remained tight-lipped about potential candidates, although the Guardian understands the former Manchester City Women manager Nick Cushing was one of the candidates identified quickly as being of interest. However, Cushing has politely appeared to rule himself out, speaking on the record. He is clearly happy and settled at New York City and there has been zero flirting for the Arsenal job from his camp.

But this job will be highly attractive to a pool of elite, world-class, experienced managers. Arsenal should take their time. After seeing Chelsea win the title five times in a row, this is a decision they cannot afford to get wrong.