A 15-year-old midfielder, Spanoudakis has reportedly attracted interest from a number of Europe's top clubs having impressed during his time with the Liga giants, whom he joined when he was just nine.
Arsenal are keen to sign Spanoudakis to permanent forms and negotiations with Barcelona over a prospective deal are understood to be continuing.
The youngster made a winning start to his spell in north London, featuring as the club's under-18 side defeated Lincoln City 1-0 on Tuesday, with Ben Sheaf on target.
And should he put pen to paper he will follow in the footsteps of six players - most notably Cesc Fabregas - by electing to swap Camp Nou for the Emirates.
Manager Arsene Wenger has already persuaded one Barcelona star to move to Arsenal this summer, Alexis Sanchez joining in a £33m deal, while Mathieu Debuchy also headed to north London from Newcastle.