Andrej Kramaric was six years old when his father, Josip, first took him to Dinamo Zagreb’s training ground. The boy had been complaining that he had no one to play football with any more: all of his friends had started school and Andrej was stuck in nursery for one more year.

“One day, Dad put me in the car and didn’t say where we were going,” Leicester City’s record signing remembers. As it turned out, they stopped just down the road, five tram stops from their home in Zagreb’s Subiceva street. Initially, the Dinamo youth coaches told him to go away and “grow up a bit” as he was much smaller than the other kids but Josip managed to persuade them to let him join in and it did not take long before they realised that while he was small for his age, he was faster than anyone else there and possessed a technique well beyond his age.

Those five tram stops became Andrej’s everyday journey for the next 16 years. From his first official game, when he wore a kit so big that you could not see his legs but still managed to score twice, to the summer of 2013, when he left the club, he was a Dinamo child through and through – a local boy and a hero in the making. Idolising Davor Suker early on, Kramaric developed an insatiable hunger for scoring, almost an obsession: by his own count, he scored 452 times for Dinamo youth teams from 1997 to 2009. Goals, goals, goals … they were always on his mind and he could never get enough of them.

He still has the same hunger, as his scoring record proves: 28 in 31 appearances for Rijeka this season, 30 in 41 last term. But that is not to say that Kramaric is the kind of No9 who needs his opportunities served on a plate; instead, he likes to get involved in link-up play, dropping back to get the ball or pulling wide to create space for others. In one TV interview, he said the style he wants to emulate would be “something between Mario Götze and Robert Lewandowski”.

There is no doubt, though, that he is at his best as a poacher, which probably drove Niko Kovac, the Croatia manager, to compare Kramaric to his childhood hero Suker. “He’s a genuine goal-getter,” Kovac said after giving Kramaric a debut in a September friendly against Cyprus. “And those dummies? You don’t see something like that very often – he doesn’t just beat opponents with his dribbles, he throws the whole stand off balance.” Earlier this season, failure to cope with a sharp Kramaric turn put the Dinamo defender Lee Addy in hospital, requiring knee surgery that will keep him out for six months.

Of course, Kramaric has weaknesses too. He is not the strongest of players and can get outmuscled by defenders who mark him closely – which has not often been the case in the Croatian league but could be with Leicester in the Premier League – and he does not have a huge presence in the air. There is room for improvement in the defensive aspect of his game but as he said, rather philosophically, in an interview for the Sportski.net website: “There’s an upside to every weakness. I may want to be more aggressive and maybe I get into games too cool-headed. Then again, maybe that’s exactly what makes scoring easier for me.”

He might need that cool head more than anything else as his Leicester career develops. Nigel Pearson’s side create chances but finishing has not been their strong suit in the top flight. What they need is someone apart from Leonardo Ulloa to score – and Kramaric is not only a lethal finisher but also versatile enough to play as a lone striker, or just off or even behind a centre-forward. Many of his goals so far have come from supportive roles.

The problem, however, is that the Foxes will need him to start banging them very soon and cannot afford to wait while he adapts to English football. Although Kramaric is a wonderfully gifted player – fast, technical and very clever in using space – scoring in Croatia (or even in the Europa League, a competition in which he recorded seven goals this season, including a hat-trick against Feyenoord) will not have prepared him for the trials and tribulations of a Premier League relegation battle.

There are doubts. The fee, £9.7m, is rather steep for a player still unproven at the highest level, and the superstitious will see it as a bad omen that a mediator in the transfer was Bosko Balaban of all people – the Croatian striker who had such a bad experience at Aston Villa that fans named him the club’s worst signing ever in one poll. The issue of Kramaric’s age (23) has been raised as well – these days players in Croatia generally move to big leagues earlier in their careers.

The truth is that Kramaric has not been ready until now. Obviously, he attracted interest of major European clubs as a free-scoring teenager in Dinamo Zagreb academy a few years ago, but the club would not sell him back then. However, they were impatient with his development and, as senior coaches tended to favour the more experienced players, Kramaric became impatient as well. After complaining about a lack of playing time in August 2013, he was immediately transfer-listed and Rijeka grabbed him on the last day of the transfer window.

So it was only after the Zagreb-born and bred kid moved away from home that his career really took off, as he has been constantly improving under the tutelage of Rijeka’s respected Slovenian coach, Matjaz Kek. Now he is already considered a valuable member of the national team, perhaps even a starter, scoring twice in his four appearances so far. Goals, goals, goals … they have flowed steadily for Kramaric, but that has not made him complacent.

“I want to do more,” he told Uefa’s website before the transfer window opened. “This is not the pinnacle for me. I am working hard and believe I can be even better.”

Aleksandar Holiga is a freelance football writer from Croatia. @AlexHoliga