The right-back has been touted as a long-term replacement for Dani Alves, who left the Nou Camp for Juventus in the summer.
The Gunners have remained adamant the 21-year-old is not for sale while the player has stated he is happy in London.
And now, according to Mundo Deportivo, Barcelona have scrapped plans to try and sign Spain international Bellerin.
The La Liga champions are aware of Arsenal’s reluctance to part with the defender and do not want to be held to ransom when trying to bring him in.
Barcelona have also been impressed by the development of Sergi Roberto, who has shifted from midfield to right-back for both club and country.