The Gunners had the Czech striker on trial when he was 14 and had planned to sign him once when he turned 16.
However, Graicier has explained how injuries thwarted his dream move.
"It's one of the best clubs in the world," the 18-year-old told Italian outlet CalcioMercato.
"I arrived in London when I was a 14-year-old. I played with the Under18 team, the Under20s and with Arsenal second team.
"After a few months of trials [Arsene] Wenger told me that I was an interesting player and that he thought he would have signed me on a permanent deal.
"In that moment, however, it was not possible for me because under the FIFA rules, a club can only sign a player after that he has turned 16.
"I waited for a year and a half but when the moment had come I got injured and I had to remain on the sidelines for more than one year.
"Arsenal had been following me after the injury but they didn't sign me in the end."