Reports in Spain today claim that the 23-year-old, who is out of contract at the end of the season, is being monitored by both Barca and their arch-rivals Real Madrid.
Both sides are aware of the quality of the player, who is known simply as 'Kepa', and the opportunity to sign the player on a free is likely to be difficult to turn down.
The problem for both sides, if you can call it a problem, is that they both already possess a quality 'keeper, namely Marc-Andre Ter Stegen and Keylor Navas and Kepa is unlikely to make the move unless he is guaranteed regular football.
Ter Stegen only signed a new contract in May, which will see him remain tied to the club until June 2022, whilst Real boss Zinedine Zidane is a huge admirer of Navas' talents.
That's without mentioning the David De Gea situation, with Real still keen on bringing him to the Spanish capital at some point in the future.
Despite both sides already possessing an excellent option between the sticks, Barca are thought to be the most likely to make a move for the player, who has made a whopping 22 appearances for spain's U21 side.
Arrizabalaga has started all but one of Athletic Bilbao's league games so far this season and many believe he will go on to be Spain's No 1 goalkeeper in the future.