The 16-year-old currently plays for NK Kustosija in Croatia.
They are demanding a £5million fee and a percentage of any future sale to agree to offloading the striker.
Man Utd have been tracking him for months but the Gunners have stepped up their interest.
Mikel Arteta sent scouts to Croatia to watch him play in his last three appearances with the club weighing up a January bid.
Klapija and his family are discussing his pending transfer and they reportedly prefer Arsenal‘s pathway than United’s.
Chelsea, RB Leipzig, Borussia Dortmund and Juventus also have te starlet on their radars.
Klapija was previously on the books of MLS side New York City but moved to NK Kustosija when his family returned to live in Croatia.
He is eligible to play for the Balkan nation as well as the United States.
And the Americans called him up to their Under-17s squad earlier this month.
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Arsenal are focusing on building for the future after their Under-18s side made the FA Youth Cup final last season.
They have been working hard to tie down their talented youngsters such as Amario Cozier-Duberry and Myles Lewis-Skelly.
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