But the England international insists he will not let his dream get to his head.
“It’s nice to hear people talking about me being England captain one day,” Jones told United’s official website.
“But I need to keep my feet on the ground and firstly play well for Manchester United. If I do that, then I’ll keep getting the chance to play for England.
“If I could captain England one day then I think that would be the pinnacle of my career.”
Jones has recently been compared with United legend Duncan Edwards.
“It’s incredible to be compared with Duncan Edwards,” he said. “He played for United and England well before my time of course but I knew about him when I was growing up.
“Even to be mentioned in the same sentence as him is a huge honour. It inspires me to go on and become a better player,” he continued. “It makes me want to work even harder in training.”
