The central midfielder, 23, was heavily linked with a move to the Emirates Stadium in the summer, but Arsene Wenger chose not to tinker with his team beyond the solitary signing of goalkeeper Petr Cech.
In a statement that will surely not fall on deaf ears at Arsenal, William has claimed that the era of the Invincibles made him love the Gunners and the Portugal international hinted at a future move to the Premier League.
"I am where I want to be right now, which is Sporting, but if I ever do leave then it's a sign that my work here was well done," he told A Bola. "I dream of winning the Primeira Liga here.
"I prefer not to say too much, but there is a club with which I’ve always been fond of: Arsenal. Because of Thierry Henry, a player with whom I have always enjoyed watching.
"Maybe this is why I look with so much affection to the Premier League."
William, who won the award for the best player at this year's European Under-21 Championship, has a contract at Sporting which expires on June 30, 2018.