Career
He is currently a youth coach at Football Club Basel. Stöckli came through the ranks at Football Club Basel and signed a professional contract with the club in 1996. Despite looking to have a bright future there, he left for Football Club Winterthur in January 2000.
He found first team opportunities few and far between at Winterthur, however, and joined Football Club Saint Gallen a season later where he became a first team regular at the relatively young age of 24.
Saint Gallen were relegated from the Swiss Super League in 2002 but Stöckli did not go down with them as he joined newly promoted club Air Corps Lugano. After just one season at Lugano, which he spent mostly on the bench, he joined Football Club Sion.
In the search for first team football he signed for Football Club Concordia Basel in 2004 and later Football Club Aarau in 2005 but was unsuccessful both times. He dropped down a division to sign for Football Club Winterthur for a second time in 2006 where he finally inherited the Number.
1 jersey. He did not make any appearances at Saint Jakob-Park and returned to Winterthur in May 2008.
On 15 August 2008, he rejoined Football Club Basel on a permanent contract after former reserve goalkeeper, Louis Crayton, departed to District of Columbia United. He was also a goalkeeping coach at Football Club Basel. He retired at the end of the 2008/09 season and became a youth coach at Basel.