Marchisio has come through the academy at Juventus to become an integral part of a formidable midfield, which has helped the Serie A champions go an astonishing 45 league matches unbeaten.
The 26-year-old told Tuttosport that he wants to stay in Turin for the rest of his career.
He said: "My dream is that when my contract expires in 2016, Juve offer me another five-year deal to keep me here until 2021.
"People have likened me to Gerrard, and I would love to be identified with only one team just like him.
Juve play their first home Champions League match of the season on Tuesday when they host Ukrainian giants Shakhtar Donetsk.