The 16-year-old, who was born in North Hempstead in the United States, began his youth career with MLS side New York City.
Despite appearing for the USA at youth level, Klapija decided to move to Croatia, where he holds citizenship through his family.
The youngster initially joined domestic champions Dinamo Zagreb, before he joined fellow Croatian side NK Kustosija.
The prospect supposedly started his career as a midfielder, before moving further forward, as he looks to develop his talents as a striker.
Klapija, who has represented Croatia at Under-17 level, is yet to make an appearance in senior football, but he is already being linked with a number of Europe's biggest clubs.
According to the Daily Mail, Premier League trio Arsenal, Man United and Chelsea are also targeting a move for the teenager.
While Man United and Chelsea are both been tracking the player's progress, Arsenal are said to be leading the race out of the three Premier League clubs.
Arsenal scouts have watched Klapija's last three games, and they are now considering a January move for the forward.
The report indicates that Arsenal's biggest competition could come from Germany, with Borussia Dortmund and RB Leipzig showing an interest.
Both clubs have developed a reputation for developing young players, which makes them appealing propositions for emerging talents.
Dortmund and Leipzig are set to step up their efforts, as they push to hold talks over a potential deal in the next month.
Kustosija are supposedly prepared to sell Klapija for a £5m fee as long as the potential deal includes a sell-on clause.
Klapija is aware of the interest and is expected to consider his options with his family in the near future.