The 28-year-old has been strongly linked with a transfer to the La Liga giants in recent months, following his exploits in America.
Giovinco ended his first season in the MLS with Toronto as their top scorer with 22 league goals and has earned a recall to the Italian national team.
While his performances have been enough to warrant attention from Barcelona, his agent has said that his importance to Toronto means that the Canadian club will not allow him to leave.
"They watched him at different times, but there was nothing concrete," Andrea D'Amico told Calciomercato.
"There was a general interest. A return to Europe? Sebastian has never considered returning. The club has made him the cornerstone of their project, they're definitely not willing to sell him.
"They want to build their team around him. Can a loan be ruled out? Yes, there's absolutely no doubt."
Giovinco has made 21 appearances for Italy, scoring his only goal in a Confederations Cup victory over Egypt in 2013.