Spanish and European champions Barcelona are thought to be monitoring Giovinco, who has taken the MLS by storm with 21 goals and 15 assists in his first season in Canada.
The 28-year-old, however, is in no rush to leave Toronto, having only departed Juventus in February.
"No, I'm happy where I am," Giovinco said when asked by Rai Sport about the link to Barcelona.
"I only just changed club, so let me enjoy this adventure first."
Giovinco was speaking after Italy's 2-1 come-from-behind win over Norway in Tuesday's final Euro 2016 qualifier.
The second-half substitute played 28 minutes in Rome.