Born in Vizzolo Predabissi, the Province of Milan, Stocchi started his career at Internazionale.
[4][5] Stocchi was promoted to Primavera team in 2008–09 season, as the backup of Slovenian Vid Belec.
However Stocchi was also named as the fourth keeper in 2008–09 UEFA Champions League as List B member (U-21 youth product).
[9] The coach of the youth team preferred to train younger footballer Nicola Maggio instead.
He followed the team relegated to the third division after Inter gave up the remain 50% registration rights to Piacenza.