The 24-year-old enjoyed a strong campaign for the Basque club, scoring four goals and providing five assists in 30 LaLiga appearances. His standout moment came in the Copa del Rey final, where he scored the opening goal as Real Sociedad beat Atletico Madrid to lift the trophy.
Barrenetxea earned his first senior call-up for Spain in March, but a late-season injury cost him a place in Luis de la Fuente's World Cup squad. According to reports, Arsenal have prepared an opening bid of around €30m for the winger.
That figure sits well below the release clause Real Sociedad have set for the player, reported to be in the region of €75m. Sociedad are determined to keep hold of Barrenetxea this summer and are said to be unwilling to negotiate below that figure.
Arsenal manager Mikel Arteta is looking to strengthen his wide attacking options, with the futures of several forwards under review. Brazil winger Gabriel Martinelli's situation is being closely watched, with some close to the player expecting a possible move to continental Europe. Should Martinelli depart, Arsenal may need to bring in more than one new winger to maintain depth across the front line.
Barrenetxea is a graduate of Real Sociedad's Zubieta academy, one of the most productive youth set-ups in Spanish football. He made his first-team debut in December 2018, becoming the club's youngest debutant since 1934 at the age of 16 years and 359 days.
He has since gone on to become a regular for the first team, known for his direct running and ability to create chances from wide areas. Notably, Barrenetxea played alongside current Arsenal midfielder Martin Zubimendi during his time progressing through Real Sociedad's ranks.
Arteta himself has connections to the same academy system, having joined Barcelona's youth setup from Antiguoko, a club in his hometown of San Sebastian, before later representing Real Sociedad.
Arsenal are understood to be assessing several attacking targets across Europe as part of their summer recruitment plans, with Barrenetxea one name among a wider list.
Tottenham have also been credited with interest in the player, adding a north London dimension to any potential pursuit. Whether Arsenal's interest develops into a formal approach is likely to depend on whether Real Sociedad show any willingness to move on their valuation.
For now, the gap between Arsenal's opening offer and Sociedad's asking price remains substantial, leaving the outcome of any pursuit firmly in the Basque club's hands.