Should he make the switch to the La Liga giants, Bellerin would join a long line of Arsenal players to swap north London for Catalonia, following the likes of Thierry Henry and Cesc Fabregas, who both secured high profile moves to the Nou Camp.
We've ranked five players who have made the move that Bellerin could soon make himself, and work out who made the best decision and who perhaps made the wrong one.
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Hleb joined the Gunners in 2005 from Stuttgart and became a bit of a utility player under Arsene Wenger.
He adapted many different midfield positions before settling on the right-wing. His debut was promising, but injuries began to stump his form.
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Despite a spell on the sidelines during his first year with Arsenal, he made 40 appearances and became the first ever Belarusian footballer to play in a Champions League final.
Hleb picked up more injuries during his time with the club and scored just seven goals in 89 appearances. Despite this, he was a popular figure amongst the fans before Barcelona made a move for the winger in 2008.
Hleb joined Barcelona for a fee of €15 million and signed a four-year contract with the Catalan giants. He featured irregularly in the first-team and made only five La Liga starts in his first season with the club, but was part of the team that won the European treble. He played in the Copa Del Ray final but did not feature in the Champions League final itself.
After a successful first year, he took the opportunity to get more game time and move on loan elsewhere, joining former club Stuttgart in 2009, before returning to the Premier League with Birmingham City in 2010.
He only made 19 appearances for Barcelona before moving away permanently to Russian side Krylia Sovetov Samara in 2012 after his contract was mutually terminated by the Spanish outfit.
Song began his Arsenal career by moving on loan from Bastia in 2005 after impressing Wenger during pre-season. He joined permanently in 2006.
He moved on loan to Charlton Athletic during his first year and impressed during his time there, but couldn't save them from relegation. He returned to Arsenal and established himself in midfield becoming a key part of the team, complimenting teammate Cesc Fabregas perfectly.
Over five years, he made 138 appearances for the club, scoring a handful of times from a defensive midfield position. However, with Arsenal failing to win a trophy since 2005, Song's desire for major honours eventually led him away from London.
The Cameroonian international joined Barcelona in 2012 for £15 million. He featured regularly during his first season, playing 20 times in La Liga as the Spaniards went on to win the whole thing. He was also an unused substitute in the 2014 Copa Del Ray final, which Barcelona lost to their rivals Real Madrid.
After just two years, he moved back to the Premier League and joined West Ham United on loan. He spent two consecutive seasons in east London, before joining Rubin Kazan permanently earlier this year.
Like Bellerin, Fabregas was a prospect of Barcelona's world famous La Masia academy, but moved to England in 2003 sensing limited opportunities.
During eight years with Arsenal, the midfielder established himself as one of the club's greatest ever modern era players. He rose up through the starting XI and became club captain in 2008.
Fabregas was named in the PFA Team of the Year twice and was included in the UEFA Team of the Year twice as well.
He made 212 appearances for Arsenal and was part of the team that won the FA Cup in 2005, but, like many other Arsenal stars, he moved away in the hope of winning more trophies.
In 2011, he moved back to Spain and rejoined Barcelona and cemented a starting place in one of the most successful teams ever. Fabregas played 151 times and scored 42 goals for Barcelona during three seasons.
He won La Liga, the Copa Del Ray, and the Spanish Super Cup during his time with the club, and won the Club World Cup in 2011.
After three successful years, he moved to Chelsea in 2014, after leaving England with unfinished trophy business, which he put right in his first year, winning the Premier League and the Capital One Cup.
Vermaelen joined Arsenal in 2009 and quickly established himself as an important player at the back for Wenger's side.
He played 110 times in five years and gained captaincy of the club in 2012. He won the FA Cup in 2014 and moved away just months later.
During his time with Barcelona, Vermaelen was plagued with injuries and struggled to establish himself in the side after spending months on the sidelines. He was in the squad that won the treble during the 2014-15 season.
He made just 21 appearances during two seasons, and could be described as a massive flop at Barcelona.
He is currently spending the season on-loan with Italian side AS Roma.
One of the greatest players to ever pull on an Arsenal shirt, Henry spent eight years in London and was a vital part of the 'Invincibles' team that went unbeaten in 2004.
He scored 226 times in 369 appearances and became Arsenal's highest ever goalscorer. He won a huge number of individual honours during his time, as well as winning the Premier League twice, FA Cup three times, and the Community Shield twice.
He moved to Barcelona in 2007, and spent three seasons with the Spanish giants during his twilight years. He managed 49 goals in 121 games and won every honour possible, including the Champions League in 2009.
He then left Barca and moved to America, before briefly returning to Arsenal on a short-term loan deal.
He has since retired from football and is now assistant manager for Belgium.
Of the five players that have made the switch from Arsenal to Barcelona, two stand out as being far more successful than the others.
Henry and Fabregas had success with both clubs and are renowned as being some of the most successful players in both England and Spain.
However, Vermaelen, Song, and Hleb were less successful after their switches to Barcelona and never quite got off the ground in Spain.
Should Hector Bellerin swap Arsenal for Barcelona? Have YOUR say in the comment section below!