The right-back has been a target for the Catalans throughout the summer as they were looking to bring the 22-year-old back to his boyhood club.
According to The Mirror, however, Bellerin has held talks with Wenger and was told there was no chance of a transfer and that he was to remain with the Gunners.
Bellerin is now expected to report for pre-season at London Colney after his extended break following Spain's 1-0 loss to Germany in the final of the U-21 European Championships.
Arsenal are also hoping to make it clear that they will not accept the Copa Del Rey champions destabilising their players anymore as they look to avoid a repeat of the Cesc Fabregas situation.
Bellerin himself recently revealed that he was unconcerned about rumours linking him to Barcelona, having only signed a six-and-a-half-year contract last November.
"I have a contract over there [with Arsenal], I have to report back for pre-season and now is the time for me to just enjoy with my team-mates in Spain for a few days," the Spaniard said.
"Enjoy time with the family, have a little break and see each other next season."
Bellerin joined the north London club from Barcelona in 2011 alongside Jon Toral as a 16-year-old and went on to become a regular in the starting eleven under Wenger during the 2014/15 season.
The La Liga side now want him back as they are still lacking a long-term replacement for Dani Alves with Sergi Roberto filling in at right-back while Aleix Vidal will miss the start of next season.