When José Mourinho was thinking of Tottenham players he might theoretically fancy buying the other day, to illustrate his point about Manchester United not being able to get their own way in the transfer market as they used to, he named Son Heung-min in addition to Harry Kane, Dele Alli and Christian Eriksen as unattainable objects of desire.

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No surprise there really; Son has been playing so well for the last few years it would be hard to find a manager who would not be interested in signing him. Yet it is easy to overlook the fact the South Korea international was not an instant hit in English football. Even after wowing German fans in his time with Hamburg and Bayer Leverkusen, even after becoming the most expensive Asian player in history with his £22m move to north London, Son was so fed up with being in and out of the Spurs team in his first season he went to see Mauricio Pochettino to ask if he could move.

Pochettino felt Son was still adjusting to the English game and encouraged him to show he had what it takes to become a first-team regular, and the rest is history. Perhaps not history in terms of trophies, medals and unarguable achievement – as Arsenal demonstrated at the weekend Spurs have not quite made the jump from nearly men to glory boys yet – but few would even attempt to argue Son has not been a marvellous addition to the Premier League scene.

Quite often he makes Match of the Day worth watching on his own; even when his performances are boiled down to abbreviated cameos, he generally manages to do something exceptional or unexpected. His style, based on searing pace, positional awareness and two-footed technical ability, is simply joyful to watch. A highlights tape of his three and a bit seasons in England would bring a smile to anyone’s face, with the possible exception of David Luiz.

At times, watching Son’s most notable contributions to the national pastime, it is easy to blur fact and fiction and recast him as some sort of prototype. The first ever hybrid footballer perhaps, part flesh and grass, part PlayStation. He certainly seems to be powered by a different sort of battery from everyone else and, just as Tour de France racing machines are now inspected closely because of suspicions that someone has found a way to hide an electrical motor within the tubing, it would not be an enormous shock to discover one day that Son has been operating with the benefit of bionic enhancement.

Facebook Twitter Pinterest Son Heung-min scores against Chelsea last month. Photograph: David Ramos/Getty Images

His recent performance against Chelsea at Wembley came right from the schoolboy fiction of yore, somewhere between Roy of the Rovers and Billy’s Boots. His finishing has always been confident, if sometimes less than lethal. It was entirely typical of him to score a memorable winning goal with a more difficult chance – if it could be called a chance – than a couple he had already missed. Wembley has not seen many goals like that – it was clearly an eye-opener for David Luiz too – though Wembley has not seen many players like Son.

Eriksen received most of the credit for the Spurs win against Internazionale in the next match after coming off the bench to score the only goal, though some observers felt the home side gained fresh impetus when Son took the field a few minutes earlier. Spurs had been watchful and quite passive for an hour, then suddenly Son ran straight at the Inter defence and made progress, evidently to the visitors’ surprise.

By that stage no one should have been surprised. Ever since Son’s pace made it appear James Milner was running through treacle in the 4-1 defeat of Liverpool just over a year ago – the time when he was referred to on Match of the Day as Usain Son – it has been clear the 26-year-old can be a handful to contain. On that occasion Son scored with a delightfully emphatic first-time finish.

This is not just the latest pigeon-catcher with no end product; Son knows where the goal is. Admittedly some of his efforts will go wide or over the bar but Son will not stop reaching dangerous positions ahead of defenders and he will not stop backing himself to score. That is what makes him so great to watch. You know what he is going to try and do well, mostly – but it does not make him any easier to stop.

It seems a pity, now the awards season is upon us, that there does not seem to be any official recognition for this type of talent and ability. Son may have to wait years for any silverware at Spurs and without being a winner or a World Cup star it will be difficult to dislodge the usual gong-gatherers from their places on the podium. Maybe there should be some footballing category similar to best supporting actor or perhaps a special award for services to the entertainment business.

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On the other hand Son is not one of football’s great individualists. Others are better at monopolising attention. He is first and foremost a team player, so it may be a while before he gets the spotlight to himself. Yet paradoxically he almost never goes unnoticed. In summary Mourinho had it right and here is a rare opportunity for the whole of football to agree with him. Son is the sort of player absolutely everyone would love to see in their own team.