Bellerin, who is currently sidelined until the end of 2019, due to serious knee injury, has been highlighted by Diego Simeone as a long term replacement for Spanish international Juanfran Torres.
Right back Juanfran ended a decade at the club at the end of the season, after his contract expired, with fellow long term servants Filipe Luis, Lucas Hernandez and Diego Godin also heading out of the club.
That has left the former Inter Milan midfielder with some significant holes to fill in his squad before the start of the 2019-20 La Liga season.
The 24-year old, who spent time as a youth player at FC Barcelona, before moving to the Gunners, has four years left on his contract at the Emirates, and manager Unai Emery is unlikely to be keen to sell one of his star players, following a disappointing end to his debut season.