Jones has just returned to action from injury.
He told a fans Q&A on manutd.com: "It sounds great and it's nice if people think that one day that might happen, but there is a long way to go before I think I can even consider it as a possibility. It would be a massive achievement for me as a footballer to captain Manchester United and it would be a great honour.
"I'm honest with myself and I know I've got a lot of hard work ahead of me in my career to become the player I want to be. So I'll focus on that for now."