Young has become a near mainstay of Jose Mourinho’s first XI this season, starting 20 of Manchester United’s 28 Premier League games.
The left-back was strongly linked last summer with a big-money move to China before working his way into Mourinho’s plans.
United have the option to extend Young’s contract, as the England international will be a free agent in the summer.
But the 32-year-old insists he wants to end his career at Old Trafford.
“It’s reported every year that I am about to leave but I’ve always wanted to be here,” he told the Mail on Sunday.
“And for as long as I can, I’d like to finish my career at United.
“I’ve got that mentality to keep going and change people’s minds.”
Young even suggested he’s much fitter now than when he was 23.
He added: “I know how to play the game, I’ve got a football brain, and feel as fit and healthy as I did when I was younger.
“I’d be able to give the 23-year-old me a race.”
United meanwhile, are back in action away to Crystal Palace on Monday (8pm).